Paper Citation Record · LEDGER

Quantitative Tracy-Widom laws for sparse random matrices

As of 19 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2507.19340.

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

pith.paper-citation-record.v1
2507.19340 v1

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

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measured 60 of 60 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T23:22:29.661790Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T22:39:01.968853Z

Reference resolution

59 of 59 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d65bb3c5-ff32-48f6-8790-05628ab1e5d1 · outbound

This paper cites Dyson Brownian motion for generalβ and potential at the edge.

Quantitative Tracy-Widom laws for sparse random matrices Dyson Brownian motion for generalβ and potential at the edge

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.159830Z

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Observation 1ce3fd10-fa01-46f4-b74f-550eb9b6efcd · outbound

This paper cites Edge rigidity of Dyson Brownian motion with general initial data.

Quantitative Tracy-Widom laws for sparse random matrices Edge rigidity of Dyson Brownian motion with general initial data

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.147950Z

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Observation 5dd53df2-fa38-46ed-8c97-10cfdd576084 · outbound

This paper cites Localized phase for the Erdős-Rényi graph.

Quantitative Tracy-Widom laws for sparse random matrices Localized phase for the Erdős-Rényi graph

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.135925Z

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Observation 8abab4e5-ce4f-4b64-a661-79ddfcffde6a · outbound

This paper cites Poisson statistics and localization at the spectral edge of sparse Erdős–Rényi graphs.

Quantitative Tracy-Widom laws for sparse random matrices Poisson statistics and localization at the spectral edge of sparse Erdős–Rényi graphs

Reference 4

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Observation 2a76b497-7b19-4147-bf91-d92d366f03e2 · outbound

This paper cites Extremal eigenvalues of critical Erdős–Rényi graphs.

Quantitative Tracy-Widom laws for sparse random matrices Extremal eigenvalues of critical Erdős–Rényi graphs

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.111269Z

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Observation 5eb8f48d-640b-4c3e-b048-909c382f96e3 · outbound

This paper cites Correlated random matrices: band rigidity and edge universality.

Quantitative Tracy-Widom laws for sparse random matrices Correlated random matrices: band rigidity and edge universality

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.099495Z

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Observation f90aff31-8010-4691-a680-2c69c7e35f9b · outbound

This paper cites Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function.

Quantitative Tracy-Widom laws for sparse random matrices Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.087211Z

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Observation 0853262e-5a72-4a94-a12e-9bb357ae88ab · outbound

This paper cites Edge rigidity and universality of random regular graphs of intermediate degree.

Quantitative Tracy-Widom laws for sparse random matrices Edge rigidity and universality of random regular graphs of intermediate degree

Reference 8

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 33633dc4-c660-4664-bd79-38ee16353345 · outbound

This paper cites Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs.

Quantitative Tracy-Widom laws for sparse random matrices Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.063713Z

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Observation da61c0a7-5cc3-4c7e-8717-6aa5769a7088 · outbound

This paper cites Spectral radii of sparse random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Spectral radii of sparse random matrices

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.052719Z

Source-reported events for the cited work

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Observation 6c8af1b1-6832-4135-bfc9-21690c69dc0b · outbound

This paper cites Lectures on the local semicircle law for Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Lectures on the local semicircle law for Wigner matrices

Reference 11

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Observation 95ea34f8-645a-4aa6-ace9-02eaa54be9e7 · outbound

This paper cites Hypothesis testing for automated community detection in networks.

Quantitative Tracy-Widom laws for sparse random matrices Hypothesis testing for automated community detection in networks

Reference 12

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Observation 8b5d9750-2078-4b54-a809-10133407e55f · outbound

This paper cites Bollobás.

Quantitative Tracy-Widom laws for sparse random matrices Bollobás

Reference 13

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Observation 847d94a1-52a4-46eb-b0bc-98da28af87b7 · outbound

This paper cites Extreme gaps between eigenvalues of Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Extreme gaps between eigenvalues of Wigner matrices

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:12.016994Z

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Observation d7fba004-a140-45dd-ad01-06b29a6dd3d5 · outbound

This paper cites Edge universality of beta ensembles.

Quantitative Tracy-Widom laws for sparse random matrices Edge universality of beta ensembles

Reference 15

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Observation 29fb147f-efe9-470f-ae24-7592d0243699 · outbound

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Quantitative Tracy-Widom laws for sparse random matrices Unresolved cited work

Reference 16

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Observation 71eb8cdf-e8c9-4718-a07c-442c096ea348 · outbound

This paper cites DasGupta.

Quantitative Tracy-Widom laws for sparse random matrices DasGupta

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.979873Z

Source-reported events for the cited work

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Observation dbfd1ac5-c6b9-4561-8afe-126e6cf9068c · outbound

This paper cites Universality at the edge of the spectrum for unitary, orthogonal, and sym- plectic ensembles of random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Universality at the edge of the spectrum for unitary, orthogonal, and sym- plectic ensembles of random matrices

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.967349Z

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Observation 9f0d34e3-2a65-4f33-a070-2a6b6e9f5a9b · outbound

This paper cites Spectral statistics of Erdős-Rényi graphs I: Local semicircle law.

Quantitative Tracy-Widom laws for sparse random matrices Spectral statistics of Erdős-Rényi graphs I: Local semicircle law

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.956082Z

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Observation d71af56c-ae60-4c30-a876-f6243d45859d · outbound

This paper cites Spectral statistics of Erdős–Rényi Graphs II: Eigen- value spacing and the extreme eigenvalues.

Quantitative Tracy-Widom laws for sparse random matrices Spectral statistics of Erdős–Rényi Graphs II: Eigen- value spacing and the extreme eigenvalues

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.944258Z

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Observation 8906ead9-194a-4f1a-99cc-5a59aa7a4eb2 · outbound

This paper cites Erdős and H.-T.

Quantitative Tracy-Widom laws for sparse random matrices Erdős and H.-T

Reference 21

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Observation 10cf9522-e78f-42d9-bb6a-24b317122934 · outbound

This paper cites Rigidity of eigenvalues of generalized Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Rigidity of eigenvalues of generalized Wigner matrices

Reference 22

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Observation 3005de7c-7316-4ca6-8369-8b4a203d34be · outbound

This paper cites Exploring Network Structure, Dynamics, and Function using NetworkX.

Quantitative Tracy-Widom laws for sparse random matrices Exploring Network Structure, Dynamics, and Function using NetworkX

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.905496Z

Source-reported events for the cited work

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Observation 42e8bbc4-be3f-4cf9-885d-b37c449629f5 · outbound

This paper cites Spectral gap and edge universality of dense random regular graphs.

Quantitative Tracy-Widom laws for sparse random matrices Spectral gap and edge universality of dense random regular graphs

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.891456Z

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Observation 6a189440-8bce-429c-8350-9cc69463423d · outbound

This paper cites Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs.

Quantitative Tracy-Widom laws for sparse random matrices Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.875677Z

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Observation fb28569a-aba3-4033-b70a-1d2a3b5f2688 · outbound

This paper cites Mesoscopic eigenvalue statistics of Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Mesoscopic eigenvalue statistics of Wigner matrices

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.863792Z

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Observation 502857f7-38bf-482a-8207-9d0ba3b085b4 · outbound

This paper cites The spectral edge of constant degree Erdős-Rényi graphs.

Quantitative Tracy-Widom laws for sparse random matrices The spectral edge of constant degree Erdős-Rényi graphs

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.851206Z

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Observation 63eeb045-b6df-4ea3-81f5-5d103ef5fa2c · outbound

This paper cites Transition from Tracy–Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs.

Quantitative Tracy-Widom laws for sparse random matrices Transition from Tracy–Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.839304Z

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Observation ee5810d2-ec2a-45e5-80a1-0d6f4bd79ff7 · outbound

This paper cites Optimal Eigenvalue Rigidity of Random Regular Graphs.

Quantitative Tracy-Widom laws for sparse random matrices Optimal Eigenvalue Rigidity of Random Regular Graphs

Reference 29

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Observation e6fa4640-26f9-4f4a-8760-75c9db555120 · outbound

This paper cites Ramanujan Property and Edge Universality of Random Regular Graphs.

Quantitative Tracy-Widom laws for sparse random matrices Ramanujan Property and Edge Universality of Random Regular Graphs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T18:00:11.243215Z

Source-reported events for the cited work

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Observation a4633c67-6b9c-4bfc-8bf2-4f952f86838c · outbound

This paper cites Edge Universality of Random Regular Graphs of Growing Degrees.

Quantitative Tracy-Widom laws for sparse random matrices Edge Universality of Random Regular Graphs of Growing Degrees

Reference 31

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Source-reported events for the cited work

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Observation 82d88b01-c929-49af-aea2-28c7e12c1260 · outbound

This paper cites Edge Universality of Sparse Random Matrices.

Quantitative Tracy-Widom laws for sparse random matrices Edge Universality of Sparse Random Matrices

Reference 32

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Observation 94d3ef5d-26ba-47e8-8a6b-09ae0a839ab4 · outbound

This paper cites Spectrum of randomd-regular graphs up to the edge.

Quantitative Tracy-Widom laws for sparse random matrices Spectrum of randomd-regular graphs up to the edge

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.824740Z

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Observation 28ff171c-d7c8-4fa9-9f3b-0d0e68a723c8 · outbound

This paper cites Janson, T.

Quantitative Tracy-Widom laws for sparse random matrices Janson, T

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.807576Z

Source-reported events for the cited work

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Observation 064a96bd-698e-438a-8e6e-ab91813d2ad3 · outbound

This paper cites Fast approach to the Tracy-Widom law at the edge of GOE and GUE.

Quantitative Tracy-Widom laws for sparse random matrices Fast approach to the Tracy-Widom law at the edge of GOE and GUE

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.792701Z

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Observation 7daf0f41-7224-4026-97e3-5c5d6fc0a44c · outbound

This paper cites VF2++—an improved subgraph isomorphism algorithm.

Quantitative Tracy-Widom laws for sparse random matrices VF2++—an improved subgraph isomorphism algorithm

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.778879Z

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Observation cdde830e-9217-45f7-800b-059954ab66b5 · outbound

This paper cites Sparse random matrices: spectral edge and statistics of rooted trees.

Quantitative Tracy-Widom laws for sparse random matrices Sparse random matrices: spectral edge and statistics of rooted trees

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.766560Z

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Observation a47d26ac-c894-4c90-a72f-3dbf6e3470bc · outbound

This paper cites Anisotropic local laws for random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Anisotropic local laws for random matrices

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.754045Z

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Observation b43a5cfc-884c-4b0f-8fff-343411452443 · outbound

This paper cites Köbler, U.

Quantitative Tracy-Widom laws for sparse random matrices Köbler, U

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.742171Z

Source-reported events for the cited work

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Observation d5c972cc-b1bd-46af-9cf0-613c148d51bf · outbound

This paper cites Edge statistics of Dyson Brownian motion.

Quantitative Tracy-Widom laws for sparse random matrices Edge statistics of Dyson Brownian motion

Reference 40

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Source-reported events for the cited work

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Observation 9f3e8ca1-474b-40a8-a31c-b2da52b77631 · outbound

This paper cites The dimension-free structure of nonhomogeneous random matrices.

Quantitative Tracy-Widom laws for sparse random matrices The dimension-free structure of nonhomogeneous random matrices

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.728429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 38092677-2487-472b-9f0c-957e72beefd4 · outbound

This paper cites Higher order fluctuations of extremal eigenvalues of sparse random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Higher order fluctuations of extremal eigenvalues of sparse random matrices

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-15T18:00:11.296561Z

Source-reported events for the cited work

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Observation 66ef6070-23d4-437a-a0f9-333e3d34fc3f · outbound

This paper cites Edge universality for deformed Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Edge universality for deformed Wigner matrices

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.712321Z

Source-reported events for the cited work

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Observation 75b5a787-7d4b-432e-b670-4a90b3a83b98 · outbound

This paper cites Local law and Tracy-Widom limit for sparse random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Local law and Tracy-Widom limit for sparse random matrices

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.696895Z

Source-reported events for the cited work

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Observation 60521d36-5a7a-4c41-8ffd-75a981e51919 · outbound

This paper cites A necessary and sufficient condition for edge universality of Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices A necessary and sufficient condition for edge universality of Wigner matrices

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.683237Z

Source-reported events for the cited work

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Observation 2642d67e-c139-45a8-b280-8d025017dc2b · outbound

This paper cites A goodness-of-fit test for stochastic block models.

Quantitative Tracy-Widom laws for sparse random matrices A goodness-of-fit test for stochastic block models

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.668715Z

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Observation e4b09439-ddc8-4c34-84b8-bcc8a57b6001 · outbound

This paper cites Edge statistics for random band matrices.

Quantitative Tracy-Widom laws for sparse random matrices Edge statistics for random band matrices

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-15T18:00:11.317592Z

Source-reported events for the cited work

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Observation 683cab5d-5957-4c9b-8b2d-c432b9a74a3f · outbound

This paper cites Algorithm 1021: SPEX Left LU, exactly solving sparse linear systems via a sparse left-looking integer-preserving LU factorization.

Quantitative Tracy-Widom laws for sparse random matrices Algorithm 1021: SPEX Left LU, exactly solving sparse linear systems via a sparse left-looking integer-preserving LU factorization

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.656481Z

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Observation 9760bbf4-f729-40ab-a480-858f481cbb58 · outbound

This paper cites On the lower bound of the spectral norm of symmetric random matrices with independent entries.

Quantitative Tracy-Widom laws for sparse random matrices On the lower bound of the spectral norm of symmetric random matrices with independent entries

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.644965Z

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Observation 2606230b-4486-4203-9b13-ece1f702a76f · outbound

This paper cites Wigner random matrices with non-symmetrically distributed entries.

Quantitative Tracy-Widom laws for sparse random matrices Wigner random matrices with non-symmetrically distributed entries

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.633770Z

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Observation c858ebda-73c3-40b2-b74a-22a94462a754 · outbound

This paper cites Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.621644Z

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Observation 61cd4e9d-d108-49cd-bca1-a26a5eab8100 · outbound

This paper cites Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.609059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1704820a-c8d8-47e4-ba25-2fba7ef66018 · outbound

This paper cites The spectral edge of some random band matrices.

Quantitative Tracy-Widom laws for sparse random matrices The spectral edge of some random band matrices

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.596598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e7c1056c-3f05-4da8-9818-3710e63cf44c · outbound

This paper cites Universality at the edge of the spectrum in Wigner random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Universality at the edge of the spectrum in Wigner random matrices

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.581358Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a6e144fc-f266-4908-8ea5-7439b6d2c6dc · outbound

This paper cites Random matrices: universality of local eigenvalue statistics up to the edge.

Quantitative Tracy-Widom laws for sparse random matrices Random matrices: universality of local eigenvalue statistics up to the edge

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.567034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 79249518-9e02-4a44-aaf7-0f04fe4e1071 · outbound

This paper cites Outliers in spectrum of sparse Wigner matrices.

Quantitative Tracy-Widom laws for sparse random matrices Outliers in spectrum of sparse Wigner matrices

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.553266Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 572efe1a-c97d-4e1d-9c04-6d2b03daefc3 · outbound

This paper cites Level-spacing distributions and the Airy kernel.

Quantitative Tracy-Widom laws for sparse random matrices Level-spacing distributions and the Airy kernel

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.536773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fe49556a-105d-4501-8da5-71288a164338 · outbound

This paper cites On orthogonal and symplectic matrix ensembles.

Quantitative Tracy-Widom laws for sparse random matrices On orthogonal and symplectic matrix ensembles

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.520903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 44dca746-cca6-4d15-a24e-a8891125098d · outbound

This paper cites Spectral norm of random matrices.

Quantitative Tracy-Widom laws for sparse random matrices Spectral norm of random matrices

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:11.506404Z

Source-reported events for the cited work

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Pith citing papers

Observation af475524-51be-43cf-9e35-5c64623fd01b · inbound

Order statistics for edge eigenvectors of Wigner matrices cites this paper.

Order statistics for edge eigenvectors of Wigner matrices Quantitative Tracy-Widom laws for sparse random matrices

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-07-03T22:39:01.970049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.