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Paper Citation Record · LEDGER

Products of Complex Rectangular and Hermitian Random Matrices

As of 17 August 2026, this Paper Citation Record lists 86 of 86 outbound references and 0 inbound Pith citation observations for arXiv:1908.09408.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.09408 v2

Coverage vector

measured 86 of 86 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:22:09.306397Z

measured 86 of 86 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

86 of 86 outbound references displayed

  • verified exact16
  • verified fuzzy26
  • unresolved43
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 75573c0a-5f8a-4507-ac17-e0732fbc07ac · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 1

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:08.953560Z digest=sha256:2779d7c343a58e9cb9b6547ced3f1ae0de10014c5ddcd897c1967926bf8d21bc

Observation df356251-d2ec-4583-a878-7c89f7313c80 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 2

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source=pdf_text observed=2026-08-14T11:22:08.959791Z digest=sha256:e3dbb2403b1a05c2e7bae6caab0ba8e143e5d12fc8737f18bbf8907b3d69347f

Observation 71616dcb-c4db-41b3-9a37-2d22e0b058d9 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 3

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:08.965107Z digest=sha256:68714bba5028ddab5fd513c2e0e4f46b8b5e3bac625c2b41b7bf69315998008b

Observation 18d88385-34d6-4b45-b032-ae8224882db2 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 4

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source=pdf_text observed=2026-08-14T11:22:08.970205Z digest=sha256:6babd94e959a9318ee532bcc5b78d91e149f0eff351099813d5381a9862b0c6c

Observation a95198cc-c335-469a-a7e5-97dfdfcf42e6 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 5

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source=pdf_text observed=2026-08-14T11:22:08.975213Z digest=sha256:77cbd19776bc1b6386733dc26d60acf485bb43a69285729ee73bce77d7c51356

Observation 68b5293b-c4e3-4e94-b92a-57bd8760cc1a · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 6

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source=pdf_text observed=2026-08-14T11:22:08.979332Z digest=sha256:38cac53912a764b7ce51f554bb55e102f5684b9aa49830fa368620efb815c632

Observation e6f48f0c-542e-4d35-8552-c6eb5982b3d3 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 7

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:08.983617Z digest=sha256:5fd3e579eeff68dc355b32b440ce191e773608b06136d5dce62e60f791bf904d

Observation 2ac177d4-3c3e-4960-b0d6-c0170a19f1d2 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 8

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source=pdf_text observed=2026-08-14T11:22:08.988006Z digest=sha256:9a44995b3d58f1c85ac9687cc2d9a6b8d66ad904ff947378e6b8f36b0674183a

Observation 3b2beac9-0e87-4557-b585-037136314c90 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 9

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source=pdf_text observed=2026-08-14T11:22:08.992356Z digest=sha256:5bd00a69b5a7120e0634eb8204a61730253d4627bd79b7143348aa14a702d2a8

Observation a15323d5-4f84-4107-adca-0a3903417e4b · outbound

This paper cites , sn) ∈ Cn and L = diag (L1,.

Products of Complex Rectangular and Hermitian Random Matrices , sn) ∈ Cn and L = diag (L1,

Reference 10

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source=pdf_text observed=2026-08-14T11:22:08.996747Z digest=sha256:10210399821b6ffd5eea43643fb35ba411375f62e3fbdf46528729e28ccc7d83

Observation 4905dffd-681f-4422-9ab5-df3b7b79fa78 · outbound

This paper cites [18, 25] for Gn, Ψ( s; g) = Φ( s, L(n); gg ∗) (18) for all s ∈ Cn and fixed L(n) as in Eq.

Products of Complex Rectangular and Hermitian Random Matrices [18, 25] for Gn, Ψ( s; g) = Φ( s, L(n); gg ∗) (18) for all s ∈ Cn and fixed L(n) as in Eq

Reference 11

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source=pdf_text observed=2026-08-14T11:22:09.001046Z digest=sha256:fb194d4b2450a70d3d679dd52bf1b129dd3c0005ff52b8eafdd2d860733a83b9

Observation e5102f4c-da82-46f4-99da-665a5fa7a257 · outbound

This paper cites al ⁄= ak and sl ⁄= sk for all l ⁄= k, and L ∈ Zn 2.

Products of Complex Rectangular and Hermitian Random Matrices al ⁄= ak and sl ⁄= sk for all l ⁄= k, and L ∈ Zn 2

Reference 12

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source=pdf_text observed=2026-08-14T11:22:09.004929Z digest=sha256:a3c3a69ac0bc9bbffdfa1ca6520f5c01797e4eb059d7ce8bc8cbc03fd5948d29

Observation 989c7096-1102-40f2-b6d1-518b69119daf · outbound

This paper cites The spherical function (18) is Ψ( s; a) =   n−1∏ j=0 j!   det[asb c ]b,c=1,...,n ∆ n(a)∆ n(s).

Products of Complex Rectangular and Hermitian Random Matrices The spherical function (18) is Ψ( s; a) =   n−1∏ j=0 j!   det[asb c ]b,c=1,...,n ∆ n(a)∆ n(s)

Reference 13

Resolution
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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.008474Z digest=sha256:e7eebed1f2aa9339adb21615895798d00374a7ff199cf57a7954555ad5e38f9a

Observation 7b24d2ba-3c84-411e-8b88-db1dd39839c8 · outbound

This paper cites 7 This theorem is proven in Appendix A 1 in a very similar way as t he real counterpart with even dimensional antisymmetric matrices in [23].

Products of Complex Rectangular and Hermitian Random Matrices 7 This theorem is proven in Appendix A 1 in a very similar way as t he real counterpart with even dimensional antisymmetric matrices in [23]

Reference 14

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source=pdf_text observed=2026-08-14T11:22:09.012063Z digest=sha256:c451c068b10e334962c13936919cb25b98cd8677c1bd9ba2501759c9ae3c21dd

Observation 5508db2e-d1e1-4989-aec6-2a4ca94cbb1f · outbound

This paper cites Additionally, we choose ˜s ∈ Cr and ˜L ∈ {0, 1}r.

Products of Complex Rectangular and Hermitian Random Matrices Additionally, we choose ˜s ∈ Cr and ˜L ∈ {0, 1}r

Reference 15

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source=pdf_text observed=2026-08-14T11:22:09.015873Z digest=sha256:b75fe1a5f7552fc138e2af5c06aa367473f6304d1a37c992d935c9bca64496af

Observation b0ed402f-e41d-4233-ae92-ad6da2aeae4b · outbound

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Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 16

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source=pdf_text observed=2026-08-14T11:22:09.020148Z digest=sha256:a4f05c3962824f69e1addcc50d5b06cb3fc7892871b4e427c85fcad1c3f7703f

Observation c1215542-def1-4a9f-8930-f18995d31c7b · outbound

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Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 17

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source=pdf_text observed=2026-08-14T11:22:09.023927Z digest=sha256:c38eac9b6ad6d0006050737e6deb62efaa18d1ccdbcaa7cf5cf110494bfce767

Observation b17588bb-f1c1-402a-8c33-fe1cc9968c59 · outbound

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Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 18

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source=pdf_text observed=2026-08-14T11:22:09.028104Z digest=sha256:08e56ef4390015354365b7061cf372384bdac7980fd7175b8d8b8f47e29f350d

Observation 2bd82224-4362-4561-a47d-ea97c9ac94a7 · outbound

This paper cites In the second equalities, we slightly abuse notation and hav e to assume that sl ⁄= sk for l ⁄= k.

Products of Complex Rectangular and Hermitian Random Matrices In the second equalities, we slightly abuse notation and hav e to assume that sl ⁄= sk for l ⁄= k

Reference 19

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source=pdf_text observed=2026-08-14T11:22:09.031736Z digest=sha256:378bbb6fdba803c8277c9582383f199728b449a28f3a7198f9804fda490d13c8

Observation fbb31e2e-ed27-49f3-b32c-3ca693806596 · outbound

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Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 20

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source=pdf_text observed=2026-08-14T11:22:09.035601Z digest=sha256:b3545d50892b5fa9cedd6d6aac84c180f3cde4b90cde7648c6697a956b91e627

Observation 79287983-8479-4cda-ae1f-6fb281ff594a · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 21

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source=pdf_text observed=2026-08-14T11:22:09.039687Z digest=sha256:f472d3d787030d443bdc8a99171f11e5d8144d2fe0d40fc0e48fa28482b400b2

Observation 18a654c2-6baa-426c-aea7-2ef7e0e52fcc · outbound

This paper cites The spherical transform SΦ is injective and, hence, invertible when restricted to its image.

Products of Complex Rectangular and Hermitian Random Matrices The spherical transform SΦ is injective and, hence, invertible when restricted to its image

Reference 22

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source=pdf_text observed=2026-08-14T11:22:09.043375Z digest=sha256:6eaf4e40ea274fa1e80d341d3362c4c8ed2f6a6197c608e2d27018403d57cfb8

Observation a98fce84-2db0-4f5f-91b4-238dbf4b8b41 · outbound

This paper cites For Gn this statement is equal to the one in [25].

Products of Complex Rectangular and Hermitian Random Matrices For Gn this statement is equal to the one in [25]

Reference 23

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raw_fallback, observed 2026-08-14T11:22:10.165951Z

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source=pdf_text observed=2026-08-14T11:22:09.047045Z digest=sha256:4561457cdddec72ae7cf0490535fb0ca675146cf50023aaf785da76246360303

Observation 7fcf3ee9-64f6-4dab-a7eb-2fa2d26a5c61 · outbound

This paper cites , wn ∈ L1 n−1(R+) is a K-invariant ensemble whose squared singular values a ∈ A are distributed as pA(a) = 1 n! ∆ n(a) det[wb(ac)]b,c=1,...,n det[Mwb(c)]b,c=1,...,n ∈ L1 Prob(An).

Products of Complex Rectangular and Hermitian Random Matrices , wn ∈ L1 n−1(R+) is a K-invariant ensemble whose squared singular values a ∈ A are distributed as pA(a) = 1 n! ∆ n(a) det[wb(ac)]b,c=1,...,n det[Mwb(c)]b,c=1,...,n ∈ L1 Prob(An)

Reference 24

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source=pdf_text observed=2026-08-14T11:22:09.051715Z digest=sha256:30b834a9cb0626708b6a3db31aa5aedf7aa312ef972268ed48c37783dd1e074d

Observation 871adcc3-e877-4db2-a800-8e9f7264b677 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 25

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source=pdf_text observed=2026-08-14T11:22:09.055744Z digest=sha256:319261e250f8a7c5fc3be10f4765809b44ea4810ce525501bf863f82c5605774

Observation 5bcd3447-b6c5-4eac-bb03-0a87df03ac09 · outbound

This paper cites , wn ∈ L1 n−1(R) is a K-invariant ensemble whose eigenvalues a ∈ D are distributed as pD(a) = 1 n! ∆ n(a) det[wb(ac)]b,c=1,...,n det[Mwb(c, c − 1)]b,c=1,...,n ∈ L1 Prob(Dn).

Products of Complex Rectangular and Hermitian Random Matrices , wn ∈ L1 n−1(R) is a K-invariant ensemble whose eigenvalues a ∈ D are distributed as pD(a) = 1 n! ∆ n(a) det[wb(ac)]b,c=1,...,n det[Mwb(c, c − 1)]b,c=1,...,n ∈ L1 Prob(Dn)

Reference 26

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raw_fallback, observed 2026-08-14T11:22:10.133670Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.059722Z digest=sha256:89b7664e56b89741074ac0cda9eabf370423ca0bc23557e8e23abfad922575ae

Observation cb0d58f8-8939-4871-b42f-21f586670218 · outbound

This paper cites , wn ∈ L1 n−1(R+).

Products of Complex Rectangular and Hermitian Random Matrices , wn ∈ L1 n−1(R+)

Reference 27

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raw_fallback, observed 2026-08-14T11:22:10.121896Z

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source=pdf_text observed=2026-08-14T11:22:09.063535Z digest=sha256:aa9f093b427a120d225ff24476ed899cc979a62e43e2450c180dc6251bcd9108

Observation 5becf0eb-2971-420c-a5eb-603b5c383dc0 · outbound

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Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 28

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source=pdf_text observed=2026-08-14T11:22:09.067568Z digest=sha256:b51a811fe2dbf71a5603de74b5a325ccce91e673eb8882eaa9d70291eaa4e6ab

Observation 7609674b-a1f4-45cf-86c2-0b7355a8036d · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 29

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raw_fallback, observed 2026-08-14T11:22:10.099550Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.071309Z digest=sha256:bdc18858da94ec3a56411294ed9fa78ee01543d878ea4cd332180945eeed6efd

Observation 1ba8ac5c-80c3-42b8-85d7-40b0016599a8 · outbound

This paper cites (55) and Θ the Heaviside step function.

Products of Complex Rectangular and Hermitian Random Matrices (55) and Θ the Heaviside step function

Reference 30

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raw_fallback, observed 2026-08-14T11:22:10.088467Z

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source=pdf_text observed=2026-08-14T11:22:09.075091Z digest=sha256:724b0e923fb3eb8a1fb45cab4d84b6077c902ac05559e04fed9375d1eac92e4e

Observation d9697dab-bc29-472c-bea1-cd9bbbbb5e91 · outbound

This paper cites , aj−1, aj+1,.

Products of Complex Rectangular and Hermitian Random Matrices , aj−1, aj+1,

Reference 31

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raw_fallback, observed 2026-08-14T11:22:10.077536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.078763Z digest=sha256:a0a13592cb2ad1d159f9a6bd8c99a60fa3c123269bc0afb0880e9fe89d3df7dc

Observation cefbfdfc-54d0-44bb-af16-c62f0e256d1f · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 32

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unresolved
raw_fallback, observed 2026-08-14T11:22:10.066654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.082693Z digest=sha256:b33aaf85390c74f801b683ef62de126f3a876d8ff3fe08163adf54ec9b996176

Observation 44321e1d-6fdb-480d-b5b9-22fb199fb2f6 · outbound

This paper cites analytical response.

Products of Complex Rectangular and Hermitian Random Matrices analytical response

Reference 33

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raw_fallback, observed 2026-08-14T11:22:10.054485Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.086229Z digest=sha256:ad98851009dda1d5cf13ea21e112ae2d07e83f26737d2dfb5dba28ed253a66c6

Observation 80199a0a-9593-4ed2-9fd7-d9b6aa4346f1 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 34

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raw_fallback, observed 2026-08-14T11:22:10.042284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.090216Z digest=sha256:9ff98bd3aee5ab6f7296539fa8a5cedf9386c9fa182f7f4aff914bef433585f1

Observation 5a2dd46c-3d75-4747-8794-528463f89835 · outbound

This paper cites Mellin-Fourier.

Products of Complex Rectangular and Hermitian Random Matrices Mellin-Fourier

Reference 35

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raw_fallback, observed 2026-08-14T11:22:10.031145Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.094074Z digest=sha256:ae1f55d679bac7984a881c937675c81e660d5bc65e577a77fd411b005c0c46b6

Observation cf2927d3-f267-4763-8a09-7cf69a6651da · outbound

This paper cites ,0)ˆk∗ ∈ H (n) l with a ∈ Dn and absorb the diagonalizing unitary matrix in the Haar dist ributed matrix k ∈ Kn in Eq.

Products of Complex Rectangular and Hermitian Random Matrices ,0)ˆk∗ ∈ H (n) l with a ∈ Dn and absorb the diagonalizing unitary matrix in the Haar dist ributed matrix k ∈ Kn in Eq

Reference 36

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raw_fallback, observed 2026-08-14T11:22:10.019539Z

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source=pdf_text observed=2026-08-14T11:22:09.097746Z digest=sha256:4197a5507828a6bc0db3bacf33d156ba8455f69ead80f813cfc48573563145ba

Observation 5178de43-4d64-4c2b-b900-d8e180f668dd · outbound

This paper cites Thence, we only need to prove the latter.

Products of Complex Rectangular and Hermitian Random Matrices Thence, we only need to prove the latter

Reference 37

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source=pdf_text observed=2026-08-14T11:22:09.101662Z digest=sha256:ba09e9ea35652932607bf8ff71da2f80c1808866afd9d2e440d9120bd962640c

Observation d7a66ba2-74fe-4dda-8770-d5b2f70ec5c1 · outbound

This paper cites Indeed when comparing the second lines of Eqs.

Products of Complex Rectangular and Hermitian Random Matrices Indeed when comparing the second lines of Eqs

Reference 38

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source=pdf_text observed=2026-08-14T11:22:09.106082Z digest=sha256:998c92312b0d2b3d2880a6e976e0831303e57f1a3123beb5c6a2fd185f4a20b0

Observation 2a680af6-d3eb-418a-90c3-5fa40e2e7b53 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 39

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source=pdf_text observed=2026-08-14T11:22:09.109790Z digest=sha256:513d1797947cafb2cac91e01369c1af896c853d746f104ef6854fde8406ef939

Observation 1bfac595-7a14-4c4b-8c05-ebe8a414cb31 · outbound

This paper cites Comparison of Eq.

Products of Complex Rectangular and Hermitian Random Matrices Comparison of Eq

Reference 40

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source=pdf_text observed=2026-08-14T11:22:09.113531Z digest=sha256:596b6c0e24048293d9dfbae7e489169f371b9e8c8736c759791726de2e63fa7c

Observation 9b00d500-cd0b-4d4c-80f5-e07328a7a14f · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 41

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source=pdf_text observed=2026-08-14T11:22:09.117809Z digest=sha256:b3f5d2dbd57f23b2d7973451db04441c85f4596c993a46ac67e8ea3ede766953

Observation 0391cc14-32a8-4794-a766-2103d85d927f · outbound

This paper cites Determinantal point processes in the plane from products of random matrices.

Products of Complex Rectangular and Hermitian Random Matrices Determinantal point processes in the plane from products of random matrices

Reference 42

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local_arxiv, observed 2026-08-14T11:22:09.800903Z

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source=pdf_text observed=2026-08-14T11:22:09.122777Z digest=sha256:762a2c7b98753c847d91d130647f5c0c370961efcaf95bfb4e7919cf163d0823

Observation d3825d9e-0775-48bb-8f69-bea1622cf6e0 · outbound

This paper cites Akemann and Z.

Products of Complex Rectangular and Hermitian Random Matrices Akemann and Z

Reference 43

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raw_fallback, observed 2026-08-14T11:22:09.948456Z

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source=pdf_text observed=2026-08-14T11:22:09.128161Z digest=sha256:cbb5707e482cd158a91bf02176e6aa364ee2978bc9aad80bc54c000f1a3a0360

Observation f8dcb676-1133-4719-9890-0797c74e6743 · outbound

This paper cites Universal microscopic correlation functions for products of truncated unitary matrices.

Products of Complex Rectangular and Hermitian Random Matrices Universal microscopic correlation functions for products of truncated unitary matrices

Reference 44

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no resolver link, observed 2026-08-14T11:22:09.131959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:09.131959Z digest=sha256:ef3cf3b9adb51f285bf71ff15c211a9b680e85e241d21dbdc9ac9f6e5e0f8900

Observation dc97fea6-1d3b-4420-b34d-61b6b5236bd6 · outbound

This paper cites Recent exact and asymptotic results for products of independent random matrices.

Products of Complex Rectangular and Hermitian Random Matrices Recent exact and asymptotic results for products of independent random matrices

Reference 45

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source=pdf_text observed=2026-08-14T11:22:09.136210Z digest=sha256:75ef421a6ac7af38d7f1b9c38d8c43794967527ed92f7a340242d2697aac1abd

Observation 1b4133eb-75d1-4463-8299-675879c12e74 · outbound

This paper cites Products of Rectangular Random Matrices: Singular Values and Progressive Scattering.

Products of Complex Rectangular and Hermitian Random Matrices Products of Rectangular Random Matrices: Singular Values and Progressive Scattering

Reference 46

Resolution
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local_arxiv, observed 2026-08-14T11:22:09.763681Z

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source=pdf_text observed=2026-08-14T11:22:09.140909Z digest=sha256:3517dbae9ec26d39cb7b9856ab0ade2c1b24ed39c09dc8e55d9ec183266a74c1

Observation 0d76240e-8ea8-479d-9b5e-4143230d5a80 · outbound

This paper cites Singular value correlation functions for products of Wishart random matrices.

Products of Complex Rectangular and Hermitian Random Matrices Singular value correlation functions for products of Wishart random matrices

Reference 47

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source=pdf_text observed=2026-08-14T11:22:09.145663Z digest=sha256:4039fde7fe61892e155f406987e9f331be0fab39621509343f91b7003a80fc5c

Observation 1b50ef28-a9ee-4165-9873-d2e15d69158c · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 48

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source=pdf_text observed=2026-08-14T11:22:09.150527Z digest=sha256:76451ae4d84879c49c47d19234ab7ff344aabc626c409c7dd4863163d7a16b35

Observation e1d44240-7696-4198-a732-aa161d27b66e · outbound

This paper cites Baryshnikov (2001): GUEs and queues , Probab.

Products of Complex Rectangular and Hermitian Random Matrices Baryshnikov (2001): GUEs and queues , Probab

Reference 49

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source=pdf_text observed=2026-08-14T11:22:09.154156Z digest=sha256:478e35ecfbcc9c34481af4de10847de358310822d218d838821b0aded02df91b

Observation 6c4dece2-a314-49dd-ba5b-01d6eda6517f · outbound

This paper cites Biorthogonal ensembles.

Products of Complex Rectangular and Hermitian Random Matrices Biorthogonal ensembles

Reference 50

Resolution
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Source-reported events for the cited work

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source=pdf_text observed=2026-08-14T11:22:09.158352Z digest=sha256:0308b7daffec180980bb3d24de7e32de94d0687fdba2450958f6ec35ae4e09c6

Observation 689ceee2-3cfe-433c-8042-7a1a22f9b6a5 · outbound

This paper cites Correlation kernels for sums and products of random matrices.

Products of Complex Rectangular and Hermitian Random Matrices Correlation kernels for sums and products of random matrices

Reference 51

Resolution
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local_arxiv, observed 2026-08-14T11:22:09.727169Z

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source=pdf_text observed=2026-08-14T11:22:09.162337Z digest=sha256:2a4209ea3f88b7b98737f8a201c1e8cc0778462ee98548a6557badc4ddb93404

Observation 82ec56e9-1c56-43f7-8c48-2adec9f3b49c · outbound

This paper cites Random and free positive maps with applications to entanglement detection.

Products of Complex Rectangular and Hermitian Random Matrices Random and free positive maps with applications to entanglement detection

Reference 52

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local_arxiv, observed 2026-08-14T11:22:09.711915Z

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source=pdf_text observed=2026-08-14T11:22:09.166668Z digest=sha256:f22d1c5e2c8c4d005c451576c6d7eb39657cfad8b01ad2eea0e81f5891118bd4

Observation d9eec2d0-0e14-476a-9eea-b5824a36d0ea · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 53

Resolution
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source=pdf_text observed=2026-08-14T11:22:09.170971Z digest=sha256:56c954be87953cd2b4855547136d3ff9c66704ebb7bf88f0c10cee749d8ebfc1

Observation 9038980c-c875-4974-97a2-df24462443ce · outbound

This paper cites Eigenvalue statistics for product complex Wishart matrices.

Products of Complex Rectangular and Hermitian Random Matrices Eigenvalue statistics for product complex Wishart matrices

Reference 54

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.695845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.174815Z digest=sha256:4b7d6a304dd9c2efeefde2967c4934f6e788e89862de1cc961281ec0fde47be9

Observation 3324c764-06c3-4dcc-9557-36f927fc88aa · outbound

This paper cites Matrix product ensembles of Hermite-type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral.

Products of Complex Rectangular and Hermitian Random Matrices Matrix product ensembles of Hermite-type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral

Reference 55

Resolution
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local_arxiv, observed 2026-08-14T11:22:09.678217Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.178886Z digest=sha256:b38661b599939ce1e1f861a8f5b9c4f50353ef4fd51cbdae6f264bda430e17fc

Observation 41248e66-ba55-413b-987c-787e704554fd · outbound

This paper cites Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles.

Products of Complex Rectangular and Hermitian Random Matrices Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles

Reference 56

Resolution
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local_arxiv, observed 2026-08-14T11:22:09.659650Z

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source=pdf_text observed=2026-08-14T11:22:09.182784Z digest=sha256:2cdb7ded6d6ddf4d3bc2eea0a6414f601ccd0930cd1c94d93a214b68dfccdcae

Observation 8c2e1db0-7dd6-4e36-b4e7-0b169d7321be · outbound

This paper cites Polynomial Ensembles and P\'olya Frequency Functions.

Products of Complex Rectangular and Hermitian Random Matrices Polynomial Ensembles and P\'olya Frequency Functions

Reference 57

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source=pdf_text observed=2026-08-14T11:22:09.186850Z digest=sha256:459a65ff8a7b3279237053b40de1e79b2853c5e9aaf4cc3d3f30470aa91f607a

Observation 60a5fa2d-d593-457f-821c-ca4f2b8b3a58 · outbound

This paper cites Products of Many Large Random Matrices and Gradients in Deep Neural Networks.

Products of Complex Rectangular and Hermitian Random Matrices Products of Many Large Random Matrices and Gradients in Deep Neural Networks

Reference 58

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source=pdf_text observed=2026-08-14T11:22:09.191284Z digest=sha256:cb5f635e9b724c5c6630d426a0a4532776475436341fdf7d19aeb248a39b7cab

Observation e3270a98-2c16-4b14-84fb-62b7b9fd3201 · outbound

This paper cites Helgason (2000): Groups and Geometric Analysis.

Products of Complex Rectangular and Hermitian Random Matrices Helgason (2000): Groups and Geometric Analysis

Reference 59

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source=pdf_text observed=2026-08-14T11:22:09.195166Z digest=sha256:5054f98aac2531f877319188ad1a136bd3eba761e5480ff6f312e49f4bb1ace9

Observation 9cd2e278-5fe5-415d-b28b-77fd5c87f617 · outbound

This paper cites Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices.

Products of Complex Rectangular and Hermitian Random Matrices Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices

Reference 60

Resolution
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source=pdf_text observed=2026-08-14T11:22:09.198748Z digest=sha256:068bd2521c9968c647ca415a77941f9a56a151ec5fcfdd6a05bac82456fb89ce

Observation 7b1b919a-4184-4fa6-98a0-7de025848d35 · outbound

This paper cites Additive Matrix Convolutions of P\'olya Ensembles and Polynomial Ensembles.

Products of Complex Rectangular and Hermitian Random Matrices Additive Matrix Convolutions of P\'olya Ensembles and Polynomial Ensembles

Reference 61

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local_arxiv, observed 2026-08-14T11:22:09.607646Z

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source=pdf_text observed=2026-08-14T11:22:09.202509Z digest=sha256:7dfea3f5099be71e6e7357c1a4873fc0ad0c685de5ed07aec358d77755500655

Observation 7f4c67bc-de8d-48d5-bfe4-2c027bd2c245 · outbound

This paper cites Hard Edge Statistics of Products of P\'olya Ensembles and Shifted GUE's.

Products of Complex Rectangular and Hermitian Random Matrices Hard Edge Statistics of Products of P\'olya Ensembles and Shifted GUE's

Reference 62

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verified exact
local_arxiv, observed 2026-08-14T11:22:09.591327Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.207277Z digest=sha256:94761f8a5a3834ee28ba57949c6ac090e69101ff29cc0ee1f3ef60e71086d644

Observation 04e60c8d-8b89-4b0b-9c5b-f3a272540480 · outbound

This paper cites Closed-form performance analysis of linear MIMO receivers in general fading scenarios.

Products of Complex Rectangular and Hermitian Random Matrices Closed-form performance analysis of linear MIMO receivers in general fading scenarios

Reference 63

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.575904Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.211427Z digest=sha256:eb715bfe487c54060fdc56a1aa8176d17209a655bfa5f34c4acf30d6f70a2d22

Observation e9f6112b-c9fb-4eed-b380-15d79712b812 · outbound

This paper cites Multiplicative Convolution of Real Asymmetric and Real Antisymmetric Matrices.

Products of Complex Rectangular and Hermitian Random Matrices Multiplicative Convolution of Real Asymmetric and Real Antisymmetric Matrices

Reference 64

Resolution
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local_arxiv, observed 2026-08-14T11:22:09.558215Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.215462Z digest=sha256:7019e5d4599b21b2968361e1c9643434b7084874f7bd717529816c93e95f4bf1

Observation 0757e010-1f8e-4485-9261-bd5ce1efd88f · outbound

This paper cites Derivation of determinantal structures for random matrix ensembles in a new way.

Products of Complex Rectangular and Hermitian Random Matrices Derivation of determinantal structures for random matrix ensembles in a new way

Reference 65

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:09.219582Z digest=sha256:61dcd05169df76a8a7373cbbe8c16f398555a66ca7cef0eba97435bec3c97bb0

Observation d5ae33d9-12a4-447c-ad75-bd3bcfc716a9 · outbound

This paper cites Exact Relation between Singular Value and Eigenvalue Statistics.

Products of Complex Rectangular and Hermitian Random Matrices Exact Relation between Singular Value and Eigenvalue Statistics

Reference 66

Resolution
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no resolver link, observed 2026-08-14T11:22:09.223821Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:09.223821Z digest=sha256:c46d78e3ec01a00acd7618c985e1ee140e9dfceca80a82b25ac9c1d3d202c357

Observation 7c60365e-a108-4c5e-8cdc-94b075128bee · outbound

This paper cites Products of Random Matrices from Polynomial Ensembles.

Products of Complex Rectangular and Hermitian Random Matrices Products of Random Matrices from Polynomial Ensembles

Reference 67

Resolution
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source=pdf_text observed=2026-08-14T11:22:09.227467Z digest=sha256:241289fb46aabbde8f1e213bac78b4d6af25963bf36fb7ca03640e5add73795b

Observation 5471e56e-e8ad-4c4c-b708-eaa1784713c1 · outbound

This paper cites Singular value statistics of matrix products with truncated unitary matrices.

Products of Complex Rectangular and Hermitian Random Matrices Singular value statistics of matrix products with truncated unitary matrices

Reference 68

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source=pdf_text observed=2026-08-14T11:22:09.232300Z digest=sha256:5c4ea0d5eb26d61712919dbd10c92f5cd20ff2c2b6a22345e82932d52fb82314

Observation f79ccbdb-c7f1-4b79-b9b6-cdadea3e7e88 · outbound

This paper cites Transformations of polynomial ensembles.

Products of Complex Rectangular and Hermitian Random Matrices Transformations of polynomial ensembles

Reference 69

Resolution
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no resolver link, observed 2026-08-14T11:22:09.237221Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:09.237221Z digest=sha256:5e2802d85bd87804f3df61e7e943c4c120e1d6e86d1b0674e1efa58897ad7012

Observation 3184a167-f653-4018-82be-90f65d0ede37 · outbound

This paper cites Spherical functions approach to sums of random Hermitian matrices.

Products of Complex Rectangular and Hermitian Random Matrices Spherical functions approach to sums of random Hermitian matrices

Reference 70

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.481500Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.242080Z digest=sha256:4bd69ad8fb43261825d3e6a6c7550282083ba5b084f1c97dbc642f1942e15769

Observation 705a7432-a025-4d32-9b17-703997318cd7 · outbound

This paper cites Singular values of products of random matrices and polynomial ensembles.

Products of Complex Rectangular and Hermitian Random Matrices Singular values of products of random matrices and polynomial ensembles

Reference 71

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no resolver link, observed 2026-08-14T11:22:09.246076Z

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source=pdf_text observed=2026-08-14T11:22:09.246076Z digest=sha256:350b4d48bf56b8c9493ef062035f0f0d1c4ccd9b24f72e4f6e4c8885e795d921

Observation 0cc35b77-7154-4636-bbd3-b046136b14db · outbound

This paper cites Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits.

Products of Complex Rectangular and Hermitian Random Matrices Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits

Reference 72

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source=pdf_text observed=2026-08-14T11:22:09.250210Z digest=sha256:846d87be56da5cc8bb6002b4c342088b4b4691e9f0be49e4298fd21eda415af6

Observation 341dd391-e88d-4ebc-bd88-bf8f2cd3d29d · outbound

This paper cites On the number of real eigenvalues of products of random matrices and an application to quantum entanglement.

Products of Complex Rectangular and Hermitian Random Matrices On the number of real eigenvalues of products of random matrices and an application to quantum entanglement

Reference 73

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.439375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation e617b4ed-fae0-4b6b-96ca-30432ea5661b · outbound

This paper cites The Dynamics of Learning: A Random Matrix Approach.

Products of Complex Rectangular and Hermitian Random Matrices The Dynamics of Learning: A Random Matrix Approach

Reference 74

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.423345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f1225f03-8b63-4640-9606-a9ecb95460ef · outbound

This paper cites Spectral statistics for product matrix ensembles of Hermite type with external source.

Products of Complex Rectangular and Hermitian Random Matrices Spectral statistics for product matrix ensembles of Hermite type with external source

Reference 75

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.406999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 32ec8073-5f94-4341-80a7-feba1b5bdf52 · outbound

This paper cites Universality for products of random matrices I: Ginibre and truncated unitary cases.

Products of Complex Rectangular and Hermitian Random Matrices Universality for products of random matrices I: Ginibre and truncated unitary cases

Reference 76

Resolution
unresolved
no resolver link, observed 2026-08-14T11:22:09.267387Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:09.267387Z digest=sha256:28d545fadf68705a318d0774edccd9c6eb47b7666b99392360b3992515b1ad99

Observation 75444a40-8af8-40be-92be-0216ad610a30 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 77

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:22:09.885898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation f316d322-3e6c-45e2-8eae-643ea6e65206 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 78

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:22:09.874381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.275554Z digest=sha256:0d8d54d322bee6e00e8ec0878cbf7d0f4e5064ee582f1db5a317d669a8ebf97e

Observation 5a7b968d-5178-4c96-a1c9-74c6028dc075 · outbound

This paper cites Pólya (1913): Über Annäherung durch Polynome mit lauter reellen Wurzeln , Rend.

Products of Complex Rectangular and Hermitian Random Matrices Pólya (1913): Über Annäherung durch Polynome mit lauter reellen Wurzeln , Rend

Reference 79

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:09.861988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.279169Z digest=sha256:3d5f13449126c4f394208c915f00c36ed0893bc6917eeb32eb527a636c454454

Observation 8689027d-3de7-45e1-ab79-07ad34b28580 · outbound

This paper cites Pólya (1915): Algebraische Untersuchungen über ganze Funktionen vom Ges chlechte Null und Eins , Journal für Math- ematik 145, 224–249.

Products of Complex Rectangular and Hermitian Random Matrices Pólya (1915): Algebraische Untersuchungen über ganze Funktionen vom Ges chlechte Null und Eins , Journal für Math- ematik 145, 224–249

Reference 80

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:09.849526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.282925Z digest=sha256:05ec54d35e26741c7bb6fd6090672a767eb40a3476f70c12195f42dbb0989344

Observation d41c3ba1-9ed6-4dcf-a20c-8219e2592062 · outbound

This paper cites Composition of quantum operations and products of random matrices.

Products of Complex Rectangular and Hermitian Random Matrices Composition of quantum operations and products of random matrices

Reference 81

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.379602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.286654Z digest=sha256:ee44f5ae08fe192a406118e9389199559d90be0ae9a570ef7193f5cc39fcc742

Observation 3953b662-8ed5-47d1-a2e9-80c2a9af172f · outbound

This paper cites Free Probability Theory.

Products of Complex Rectangular and Hermitian Random Matrices Free Probability Theory

Reference 82

Resolution
unresolved
no resolver link, observed 2026-08-14T11:22:09.290851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T11:22:09.290851Z digest=sha256:c0837a9864c037b09914671d1ab6980b13014f0011df5b954660ddcaca969448

Observation 39da0d38-213f-4a44-8c9b-d01ac30de7b4 · outbound

This paper cites Dynamical Isometry is Achieved in Residual Networks in a Universal Way for any Activation Function.

Products of Complex Rectangular and Hermitian Random Matrices Dynamical Isometry is Achieved in Residual Networks in a Universal Way for any Activation Function

Reference 83

Resolution
verified exact
local_arxiv, observed 2026-08-14T11:22:09.347404Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.295080Z digest=sha256:84ba72ec0f33782dc684d4c4328768b863738b6def8429862552820a12b6acd0

Observation 28574ea0-9a80-46ba-8822-0498ae9fa6f3 · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 84

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:22:09.837824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.299130Z digest=sha256:4d258da433e4fc12e75495c403ae9301be44d14374c241c422767cf6c1ecd1dd

Observation 9b3f5626-e544-4037-b059-b0d1cfd376f8 · outbound

This paper cites Voiculescu (1991): Limit laws for Random matrices and free products , Invent.

Products of Complex Rectangular and Hermitian Random Matrices Voiculescu (1991): Limit laws for Random matrices and free products , Invent

Reference 85

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:09.825924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.302835Z digest=sha256:39c67fcfae3d96e4cc3223ab08dd673f966954959274c422f7756c1d24c22d0c

Observation 9b81bf16-842e-4d22-b25a-f142dd677cea · outbound

This paper cites an unresolved cited work.

Products of Complex Rectangular and Hermitian Random Matrices Unresolved cited work

Reference 86

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:22:09.814081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-14T11:22:09.306397Z digest=sha256:c4282979b8c0ddaf38a02327de21416e302a0d71046ac48424f4af5288fc0424

Pith citing papers

No inbound Pith citation observations are available.