Paper Citation Record · LEDGER

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon

As of 7 August 2026, this Paper Citation Record lists 100 of 118 outbound references and 4 inbound Pith citation observations for arXiv:2508.21055.

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

pith.paper-citation-record.v1
2508.21055 v1

Coverage vector

measured 100 of 118 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T14:49:16.060735Z

measured 104 of 104 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T18:20:37.905508Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T23:19:03.167574Z

Reference resolution

100 of 118 outbound references displayed

verified exact0
verified fuzzy57
unresolved43
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f2561b0c-9997-4450-a3f7-18ae1e5101bc · outbound

This paper cites Random walks on finite groups and rapidly mixing Markov chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Random walks on finite groups and rapidly mixing Markov chains

Reference 1

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Observation f34ba906-9586-4997-bf9f-b7c1823df787 · outbound

This paper cites Hitting times for random walks on vertex-transitive graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Hitting times for random walks on vertex-transitive graphs

Reference 2

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Observation 6338efb5-ef02-4650-b5fd-c86a3600d5d1 · outbound

This paper cites Shuffling cards and stopping times.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Shuffling cards and stopping times

Reference 3

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Observation 1a261e1d-3c85-4390-8183-c430ce44b760 · outbound

This paper cites Comparing with octopi.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Comparing with octopi

Reference 4

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Observation 3ea32cbb-642e-4758-92fa-efd53f2af9e0 · outbound

This paper cites Random Cayley graphs and expanders.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Random Cayley graphs and expanders

Reference 5

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Observation 5450ad0b-d74a-4c43-ac54-9227a7517ffc · outbound

This paper cites Spectral independence in high- dimensional expanders and applications to the hardcore model.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Spectral independence in high- dimensional expanders and applications to the hardcore model

Reference 6

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Observation 0c6661cd-7c17-4768-837f-1e3c627a62cb · outbound

This paper cites Metastability in a con- densing zero-range process in the thermodynamic limit.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Metastability in a con- densing zero-range process in the thermodynamic limit

Reference 7

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Observation 3cdb0ed2-1869-4094-b792-12163d315086 · outbound

This paper cites Bakry and Michel ´Emery.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Bakry and Michel ´Emery

Reference 8

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Observation 8268513c-ab2e-4649-a516-435c646f9fae · outbound

This paper cites Analysis and geometry of Markov diffusion operators, volume 348 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences].

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Analysis and geometry of Markov diffusion operators, volume 348 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]

Reference 9

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Observation 3553a719-9a24-464a-a06d-d347cea0d31f · outbound

This paper cites Characterization of cutoff for reversible Markov chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Characterization of cutoff for reversible Markov chains

Reference 10

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Observation 90213451-6441-48e4-8020-562bbb64ea64 · outbound

This paper cites Bate, Stephen B.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Bate, Stephen B

Reference 11

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Observation 7fca8d88-16a2-4075-a4fb-28c3312ed810 · outbound

This paper cites Inequalities in Fourier analysis.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Inequalities in Fourier analysis

Reference 12

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Observation 747307bc-340a-46ab-ad99-0647c189d286 · outbound

This paper cites A threshold for cutoff in two-community random graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon A threshold for cutoff in two-community random graphs

Reference 13

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Observation c809c313-0d55-4832-8f07-9faa047c42db · outbound

This paper cites Cutoff for nonbacktracking random walks on sparse random graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for nonbacktracking random walks on sparse random graphs

Reference 14

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Observation da0dde92-c1a6-47ae-8b20-8ac13b90a536 · outbound

This paper cites Cutoff for conjugacy-invariant random walks on the permutation group.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for conjugacy-invariant random walks on the permutation group

Reference 15

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This paper cites Random walks on the random graph.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Random walks on the random graph

Reference 16

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Observation 92bff8da-c4eb-4c29-b6b6-9c4abbc95d55 · outbound

This paper cites Cutoff for random to random card shuffle.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for random to random card shuffle

Reference 17

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Observation b6210437-372b-4e1d-96e5-d4de53959aa9 · outbound

This paper cites On mixing of Markov chains: coupling, spectral independence, and entropy factorization.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon On mixing of Markov chains: coupling, spectral independence, and entropy factorization

Reference 18

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Observation 63d5eb9b-bcc6-4ff3-a669-749505221a29 · outbound

This paper cites Bobkov and Prasad Tetali.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Bobkov and Prasad Tetali

Reference 19

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Observation 7396c080-9995-4447-a632-9d843bdc97d3 · outbound

This paper cites ´ etude des coefficients de Fourier des fonctions de Lp(G).

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon ´ etude des coefficients de Fourier des fonctions de Lp(G)

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T14:49:15.769151Z

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Observation 0d00562e-f3ae-4a83-a198-5d037c231a94 · outbound

This paper cites Random walk on sparse random digraphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Random walk on sparse random digraphs

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T14:49:15.772947Z

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Observation 9b2f539a-22d7-4f29-8a17-94f3b0aebc94 · outbound

This paper cites Cutoff at the entropic time for random walks on covered expander graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff at the entropic time for random walks on covered expander graphs

Reference 22

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Observation 3393bd8d-c94d-419b-8cd2-316621ecbd1e · outbound

This paper cites Oxford University Press, Oxford, 2013.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Oxford University Press, Oxford, 2013

Reference 23

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Observation 9a0220d9-6748-434b-bfe0-4b102af2b1d8 · outbound

This paper cites Mixing time of the adjacent walk on the simplex.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Mixing time of the adjacent walk on the simplex

Reference 24

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Observation 42393384-5fb7-4576-a2ee-f575f26d3fd5 · outbound

This paper cites Spectral gap and cutoff phenomenon for the Gibbs sampler of ∇φ interfaces with convex potential.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Spectral gap and cutoff phenomenon for the Gibbs sampler of ∇φ interfaces with convex potential

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-05T14:49:15.786389Z

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Observation e6ae784b-0cad-4453-a2d1-45e2fe6f86e4 · outbound

This paper cites Liggett, and Thomas Richthammer.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Liggett, and Thomas Richthammer

Reference 26

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Observation 6737b6de-6e0c-45be-82b1-1d2095df385b · outbound

This paper cites Entropy and curvature: beyond the Peres-Tetali conjecture.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Entropy and curvature: beyond the Peres-Tetali conjecture

Reference 27

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Observation e2294bea-2b68-43c7-86d7-592e552a3bb7 · outbound

This paper cites Entropy dissipation estimates in a zero-range dy- namics.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Entropy dissipation estimates in a zero-range dy- namics

Reference 28

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This paper cites On the log-Sobolev constant for the simple random walk on the n-cycle: the even cases.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon On the log-Sobolev constant for the simple random walk on the n-cycle: the even cases

Reference 29

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Observation c1ff14cc-b1d2-4a8f-8c0f-355a6094c0dd · outbound

This paper cites Optimal mixing of Glauber dynamics: entropy factorization via high-dimensional expansion.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Optimal mixing of Glauber dynamics: entropy factorization via high-dimensional expansion

Reference 30

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Observation 70872d09-26dd-40a5-91c2-3026942e9c01 · outbound

This paper cites Modified log-Sobolev inequalities for strongly log-concave distributions.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Modified log-Sobolev inequalities for strongly log-concave distributions

Reference 31

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Observation 6e57d516-1b2d-43fa-aa9b-9b31ae1563de · outbound

This paper cites Glauber dynamics for the mean-field potts model.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Glauber dynamics for the mean-field potts model

Reference 32

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Observation 2d845e28-0ad7-498c-a7e2-f1d712004ce8 · outbound

This paper cites Logarithmic Sobolev inequality for zero-range dynamics.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Logarithmic Sobolev inequality for zero-range dynamics

Reference 33

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This paper cites Diaconis and L.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Diaconis and L

Reference 34

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This paper cites Group representations in probability and statistics , volume 11 of Insti- tute of Mathematical Statistics Lecture Notes—Monograph Series.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Group representations in probability and statistics , volume 11 of Insti- tute of Mathematical Statistics Lecture Notes—Monograph Series

Reference 35

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Observation 2008a983-081d-488a-9404-2a821f051dcb · outbound

This paper cites The cutoff phenomenon in finite Markov chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The cutoff phenomenon in finite Markov chains

Reference 36

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Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The Markov chain Monte Carlo revolution

Reference 37

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This paper cites Generating a random permutation with random transpositions.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Generating a random permutation with random transpositions

Reference 38

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Observation 3d770422-3812-45ba-add9-7bb57f3daf89 · outbound

This paper cites Total variation cutoff in birth-and-death chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Total variation cutoff in birth-and-death chains

Reference 39

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Observation 41bd719f-50b9-4e61-b688-d70f0221a1fd · outbound

This paper cites Enumeration and random random walks on finite groups.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Enumeration and random random walks on finite groups

Reference 40

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This paper cites Sharp threshold phenomena in statistical physics.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Sharp threshold phenomena in statistical physics

Reference 41

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Observation d7cf56ca-5ce6-40a6-b3af-383fc0c7c654 · outbound

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Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Lee, and Joseph Lehec

Reference 42

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Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Unresolved cited work

Reference 43

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Observation ac2a1d84-832d-4aba-8a36-ea21dc758510 · outbound

This paper cites Ganguly, E.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Ganguly, E

Reference 44

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Observation aece1ef9-a767-411b-aab8-592c56b3ac30 · outbound

This paper cites Mixing times for the simple exclusion process with open boundaries, 2020.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Mixing times for the simple exclusion process with open boundaries, 2020

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.980059Z

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Observation d43a0e90-06e2-4cfd-9453-be28efee8d3b · outbound

This paper cites Exponential decay of entropy in the random trans- position and Bernoulli-Laplace models.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Exponential decay of entropy in the random trans- position and Bernoulli-Laplace models

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.969482Z

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Observation da3827b1-7653-49fd-ad31-f0e9f4637738 · outbound

This paper cites Modified logarithmic Sobolev inequalities for some models of random walk.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Modified logarithmic Sobolev inequalities for some models of random walk

Reference 47

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Observation e3964196-5a0d-4961-840e-524378b97138 · outbound

This paper cites Sharp con- vergence to equilibrium for the ssep with reservoirs, 2021.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Sharp con- vergence to equilibrium for the ssep with reservoirs, 2021

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.947551Z

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Observation cb80b034-8a2e-46ab-b90f-b6c7ad81072b · outbound

This paper cites Logarithmic Sobolev inequalities.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Logarithmic Sobolev inequalities

Reference 49

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Observation 29037ce0-4012-4f78-95b8-42dcf78fdfd9 · outbound

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Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Unresolved cited work

Reference 50

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Observation c3aba3ac-1aae-471c-a429-169251e5f60b · outbound

This paper cites Cutoff for Ramanujan graphs via degree inflation.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for Ramanujan graphs via degree inflation

Reference 51

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Observation 9918b674-2130-4533-90fb-f779a8f7e68d · outbound

This paper cites Cutoff for almost all random walks on abelian groups, 2021.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for almost all random walks on abelian groups, 2021

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.909890Z

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Observation 5a5434bc-403e-4881-afc4-c31e7f60d31d · outbound

This paper cites Cutoff for random walks on upper trian- gular matrices, 2021.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for random walks on upper trian- gular matrices, 2021

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.897915Z

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Observation b5c08d33-0bf0-473e-83ef-b2ac5f887174 · outbound

This paper cites Further results and discussions on random cayley graphs, 2021.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Further results and discussions on random cayley graphs, 2021

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.887247Z

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Observation 59182d91-c6d0-4fd2-87a5-46b30b476d04 · outbound

This paper cites Geometry of random cayley graphs of abelian groups, 2021.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Geometry of random cayley graphs of abelian groups, 2021

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.876625Z

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Observation f3dc23ed-8e76-44e2-afb0-3acaa91ef5d6 · outbound

This paper cites The exclusion process mixes (almost) faster than independent particles.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The exclusion process mixes (almost) faster than independent particles

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.865664Z

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Observation ec305e66-27ad-4e77-92dc-929ef7d1c153 · outbound

This paper cites A version of Aldous’ spectral-gap conjecture for the zero range process.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon A version of Aldous’ spectral-gap conjecture for the zero range process

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.853840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 72e0fbe9-d2ab-4520-b2ca-14bed523cc0a · outbound

This paper cites Cutoff for the mean-field zero-range process with bounded monotone rates.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for the mean-field zero-range process with bounded monotone rates

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.841984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 838ea96d-c1bf-449c-a061-31a9d92c5b31 · outbound

This paper cites Entropy dissipation estimates for inhomogeneous zero-range processes.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Entropy dissipation estimates for inhomogeneous zero-range processes

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.830560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dde153f2-87b8-4473-a3e6-54a2c79825d4 · outbound

This paper cites The interchange process on high-dimensional products.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The interchange process on high-dimensional products

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.818976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1668c8b7-d20a-4d96-aadf-6b7f05809cff · outbound

This paper cites Universality of cutoff for graphs with an added random matching.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Universality of cutoff for graphs with an added random matching

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.807886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8ae84446-1717-4110-a8b2-2d05cd129ef8 · outbound

This paper cites Cutoff for random walk on random graphs with a community structure, 2022.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for random walk on random graphs with a community structure, 2022

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.796891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c3ba4803-f73c-468e-b884-a9c96a8aa822 · outbound

This paper cites Random walks supported on random points of Z/nZ.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Random walks supported on random points of Z/nZ

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.785521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 909739ec-a822-4452-b510-e49459b07689 · outbound

This paper cites A survey of results on random random walks on finite groups.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon A survey of results on random random walks on finite groups

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.773380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d46b4fdd-367e-4e1f-aa28-7cf57059164d · outbound

This paper cites Expander graphs and their appli- cations.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Expander graphs and their appli- cations

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.762898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 035a1f6c-fc52-41d9-bfe3-32f6a4a176aa · outbound

This paper cites Riemannian geometry and geometric analysis.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Riemannian geometry and geometric analysis

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.751985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 103eb260-1bd5-446b-88b0-a80e14892095 · outbound

This paper cites The influence of variables on Boolean func- tions.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The influence of variables on Boolean func- tions

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.740959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5d075a43-4970-4605-97c3-6be2542febae · outbound

This paper cites Optimal lossless compression: Source varen- tropy and dispersion.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Optimal lossless compression: Source varen- tropy and dispersion

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.729533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 62fa13dd-5761-4da8-9415-1e308d7f8650 · outbound

This paper cites Cutoff phenomenon for the asymmetric simple exclu- sion process and the biased card shuffling.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff phenomenon for the asymmetric simple exclu- sion process and the biased card shuffling

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.717988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 07b225cf-ece3-43f0-84f3-1965d0378c62 · outbound

This paper cites The cutoff profile for the simple exclusion process on the circle.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The cutoff profile for the simple exclusion process on the circle

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.706657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7ea0674d-82fb-45f4-addb-6bb17a3a0058 · outbound

This paper cites Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.694910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5170adc3-34d0-4299-86a4-8d3a60dfb23f · outbound

This paper cites The simple exclusion process on the circle has a diffusive cutoff window.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon The simple exclusion process on the circle has a diffusive cutoff window

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.684031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 750e6649-e6a3-40fe-8cec-45b91f1d6279 · outbound

This paper cites Concentration of measure and logarithmic Sobolev inequalities.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Concentration of measure and logarithmic Sobolev inequalities

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.671511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 326a56ff-7d14-4791-97ce-133f44e265d6 · outbound

This paper cites Glauber dynamics for the mean- field Ising model: cut-off, critical power law, and metastability.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Glauber dynamics for the mean- field Ising model: cut-off, critical power law, and metastability

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.659548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2467ba28-aadb-44ca-b262-72dde29548d7 · outbound

This paper cites Coupling from the past.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Coupling from the past

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.648386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0da7f1d7-f59a-4778-95d5-4f693b4ecc71 · outbound

This paper cites an unresolved cited work.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Unresolved cited work

Reference 76

Resolution: unresolved; raw_fallback, observed 2026-08-05T14:49:16.637877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 29b56083-3faf-4c1d-a2a9-d2589c1360eb · outbound

This paper cites an unresolved cited work.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Unresolved cited work

Reference 77

Resolution: unresolved; raw_fallback, observed 2026-08-05T14:49:16.627141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 60eafde3-f64c-4f9e-b9c2-b676102b5697 · outbound

This paper cites Ricci curvature and eigenvalue estimate on locally finite graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Ricci curvature and eigenvalue estimate on locally finite graphs

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.617796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 32a9bba7-4038-45a9-bcbb-d1e091c9d662 · outbound

This paper cites Cutoff on all Ramanujan graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff on all Ramanujan graphs

Reference 79

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.608049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b1c22c82-1e41-4139-b1b5-e27fc5e81675 · outbound

This paper cites Cutoff phenomena for random walks on random regular graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff phenomena for random walks on random regular graphs

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.596703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 18d147ac-5dc6-4d07-96b4-a023c2a27ab9 · outbound

This paper cites Explicit expanders with cutoff phenomena.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Explicit expanders with cutoff phenomena

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.585996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d99acaaa-c1b6-4ba6-98ba-5dfa0da6d07c · outbound

This paper cites Cutoff for the Ising model on the lattice.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for the Ising model on the lattice

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.576140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4244ffab-c8a4-420d-a889-2c0dd8d76d0f · outbound

This paper cites Cutoff for general spin systems with arbitrary boundary conditions.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for general spin systems with arbitrary boundary conditions

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.565998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f1f8a433-fe68-47f5-add3-9cd0d1444b53 · outbound

This paper cites An exposition to information percolation for the Ising model.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon An exposition to information percolation for the Ising model

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.555102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4a0b79a8-29fa-4c43-91e9-e54314cdbdeb · outbound

This paper cites Information percolation and cutoff for the stochastic Ising model.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Information percolation and cutoff for the stochastic Ising model

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.544756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 615bdde2-e039-49d4-906f-56f0b4260b32 · outbound

This paper cites Universality of cutoff for the Ising model.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Universality of cutoff for the Ising model

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.534957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2c5e6309-8103-47f1-99d4-1104edaa2181 · outbound

This paper cites Lectures on Glauber dynamics for discrete spin models.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Lectures on Glauber dynamics for discrete spin models

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.525166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6f399eb7-949e-41a9-9675-6acccbcf80f0 · outbound

This paper cites Cutoff for the mean-field zero-range process.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for the mean-field zero-range process

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.515657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f68ced92-2ca8-4d18-a0aa-ab2cc7f90963 · outbound

This paper cites Rosenbluth, Marshall N.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Rosenbluth, Marshall N

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.506000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation fa6436a1-34af-457a-ad89-3677ef4978ec · outbound

This paper cites Mathematical aspects of mixing times in Markov chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Mathematical aspects of mixing times in Markov chains

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.495852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bb31512a-3f2f-49ff-a454-1eaf0d040964 · outbound

This paper cites Spectral gap for the zero range process with constant rate.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Spectral gap for the zero range process with constant rate

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.485366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 34a75903-a2c3-473a-88f2-75bca40d3bc8 · outbound

This paper cites Ollivier curvature, isoperimetry, concentration, and log-Sobolev inequalitiy, 2023.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Ollivier curvature, isoperimetry, concentration, and log-Sobolev inequalitiy, 2023

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.474590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4358402c-ac84-4d7c-9c83-2fc3955e599a · outbound

This paper cites Cutoff for the Swendsen-Wang dynamics on the lattice.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Cutoff for the Swendsen-Wang dynamics on the lattice

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.462721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c09b58c3-ce80-4f4c-8469-927a5cac5e64 · outbound

This paper cites On the Banach-space-valued Azuma inequality and small-set isoperimetry of Alon-Roichman graphs.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon On the Banach-space-valued Azuma inequality and small-set isoperimetry of Alon-Roichman graphs

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.450478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4c5e9522-ce36-4b2d-ae59-12c722f97790 · outbound

This paper cites Limit profiles for reversible Markov chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Limit profiles for reversible Markov chains

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.437938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3548e7aa-9583-4aa5-9fb4-307ab70631c0 · outbound

This paper cites Analysis of Boolean functions.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Analysis of Boolean functions

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.425965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f6db5208-6231-403a-a666-8242de4d4665 · outbound

This paper cites Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.412829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 62f992ad-9cb8-4d3e-a0a5-10a088141d27 · outbound

This paper cites Ricci curvature of metric spaces.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Ricci curvature of metric spaces

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.399453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation be7177f0-9b34-4d15-bdbe-241ce1b1ec66 · outbound

This paper cites Ricci curvature of Markov chains on metric spaces.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon Ricci curvature of Markov chains on metric spaces

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.386810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 68b0aa58-1f5e-4695-b370-462dbd7db89d · outbound

This paper cites A survey of Ricci curvature for metric spaces and Markov chains.

Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon A survey of Ricci curvature for metric spaces and Markov chains

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:49:16.374392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 966ad218-f636-4785-ac76-cada0bfa2896 · inbound

Long-time $L^p$ Wasserstein contraction for diffusion processes without global dissipativity cites this paper.

Long-time $L^p$ Wasserstein contraction for diffusion processes without global dissipativity Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon

Reference 44

Resolution: verified exact; arxiv_id, observed 2026-05-15T18:06:25.255515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 69dc5842-ad0a-48c1-a099-d56cda559bb8 · inbound

Log-Sobolev under random monotone censoring cites this paper.

Log-Sobolev under random monotone censoring Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-03T03:07:35.093350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 41cc52b0-78cc-4611-be63-cbd06ddd2d8a · inbound

Analysis of the asymmetric shelf shuffle cites this paper.

Analysis of the asymmetric shelf shuffle Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-03T23:19:03.170922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b1a0a913-073d-4532-951d-12ec4cdbe02a · inbound

Markov and lattice bases for Forman-Ricci curvature of graphs cites this paper.

Markov and lattice bases for Forman-Ricci curvature of graphs Modern aspects of Markov chains: entropy, curvature and the cutoff phenomenon

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T18:20:37.905508Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.