Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:00:11.369547Z
Paper Citation Record · LEDGER
As of 16 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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:00:11.369547Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-26T23:22:29.661790Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T22:39:01.968853Z
59 of 59 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation d65bb3c5-ff32-48f6-8790-05628ab1e5d1 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Dyson Brownian motion for generalβ and potential at the edge
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1ce3fd10-fa01-46f4-b74f-550eb9b6efcd · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge rigidity of Dyson Brownian motion with general initial data
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5dd53df2-fa38-46ed-8c97-10cfdd576084 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Localized phase for the Erdős-Rényi graph
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8abab4e5-ce4f-4b64-a661-79ddfcffde6a · outbound
Quantitative Tracy-Widom laws for sparse random matrices Poisson statistics and localization at the spectral edge of sparse Erdős–Rényi graphs
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2a76b497-7b19-4147-bf91-d92d366f03e2 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Extremal eigenvalues of critical Erdős–Rényi graphs
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5eb8f48d-640b-4c3e-b048-909c382f96e3 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Correlated random matrices: band rigidity and edge universality
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f90aff31-8010-4691-a680-2c69c7e35f9b · outbound
Quantitative Tracy-Widom laws for sparse random matrices Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 0853262e-5a72-4a94-a12e-9bb357ae88ab · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge rigidity and universality of random regular graphs of intermediate degree
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 33633dc4-c660-4664-bd79-38ee16353345 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Largest eigenvalues of sparse inhomogeneous Erdős–Rényi graphs
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation da61c0a7-5cc3-4c7e-8717-6aa5769a7088 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Spectral radii of sparse random matrices
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6c8af1b1-6832-4135-bfc9-21690c69dc0b · outbound
Quantitative Tracy-Widom laws for sparse random matrices Lectures on the local semicircle law for Wigner matrices
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 95ea34f8-645a-4aa6-ace9-02eaa54be9e7 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Hypothesis testing for automated community detection in networks
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8b5d9750-2078-4b54-a809-10133407e55f · outbound
Quantitative Tracy-Widom laws for sparse random matrices Bollobás
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 847d94a1-52a4-46eb-b0bc-98da28af87b7 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Extreme gaps between eigenvalues of Wigner matrices
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d7fba004-a140-45dd-ad01-06b29a6dd3d5 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge universality of beta ensembles
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 29fb147f-efe9-470f-ae24-7592d0243699 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Unresolved cited work
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 71eb8cdf-e8c9-4718-a07c-442c096ea348 · outbound
Quantitative Tracy-Widom laws for sparse random matrices DasGupta
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation dbfd1ac5-c6b9-4561-8afe-126e6cf9068c · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9f0d34e3-2a65-4f33-a070-2a6b6e9f5a9b · outbound
Quantitative Tracy-Widom laws for sparse random matrices Spectral statistics of Erdős-Rényi graphs I: Local semicircle law
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d71af56c-ae60-4c30-a876-f6243d45859d · outbound
Quantitative Tracy-Widom laws for sparse random matrices Spectral statistics of Erdős–Rényi Graphs II: Eigen- value spacing and the extreme eigenvalues
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8906ead9-194a-4f1a-99cc-5a59aa7a4eb2 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Erdős and H.-T
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 10cf9522-e78f-42d9-bb6a-24b317122934 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Rigidity of eigenvalues of generalized Wigner matrices
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3005de7c-7316-4ca6-8369-8b4a203d34be · outbound
Quantitative Tracy-Widom laws for sparse random matrices Exploring Network Structure, Dynamics, and Function using NetworkX
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 42e8bbc4-be3f-4cf9-885d-b37c449629f5 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Spectral gap and edge universality of dense random regular graphs
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6a189440-8bce-429c-8350-9cc69463423d · outbound
Quantitative Tracy-Widom laws for sparse random matrices Fluctuations of extreme eigenvalues of sparse Erdős-Rényi graphs
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fb28569a-aba3-4033-b70a-1d2a3b5f2688 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Mesoscopic eigenvalue statistics of Wigner matrices
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 502857f7-38bf-482a-8207-9d0ba3b085b4 · outbound
Quantitative Tracy-Widom laws for sparse random matrices The spectral edge of constant degree Erdős-Rényi graphs
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 63eeb045-b6df-4ea3-81f5-5d103ef5fa2c · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ee5810d2-ec2a-45e5-80a1-0d6f4bd79ff7 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Optimal Eigenvalue Rigidity of Random Regular Graphs
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e6fa4640-26f9-4f4a-8760-75c9db555120 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Ramanujan Property and Edge Universality of Random Regular Graphs
Reference 30
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4633c67-6b9c-4bfc-8bf2-4f952f86838c · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge Universality of Random Regular Graphs of Growing Degrees
Reference 31
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 82d88b01-c929-49af-aea2-28c7e12c1260 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge Universality of Sparse Random Matrices
Reference 32
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 94d3ef5d-26ba-47e8-8a6b-09ae0a839ab4 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Spectrum of randomd-regular graphs up to the edge
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 28ff171c-d7c8-4fa9-9f3b-0d0e68a723c8 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Janson, T
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 064a96bd-698e-438a-8e6e-ab91813d2ad3 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Fast approach to the Tracy-Widom law at the edge of GOE and GUE
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7daf0f41-7224-4026-97e3-5c5d6fc0a44c · outbound
Quantitative Tracy-Widom laws for sparse random matrices VF2++—an improved subgraph isomorphism algorithm
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation cdde830e-9217-45f7-800b-059954ab66b5 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Sparse random matrices: spectral edge and statistics of rooted trees
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a47d26ac-c894-4c90-a72f-3dbf6e3470bc · outbound
Quantitative Tracy-Widom laws for sparse random matrices Anisotropic local laws for random matrices
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b43a5cfc-884c-4b0f-8fff-343411452443 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Köbler, U
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d5c972cc-b1bd-46af-9cf0-613c148d51bf · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge statistics of Dyson Brownian motion
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9f3e8ca1-474b-40a8-a31c-b2da52b77631 · outbound
Quantitative Tracy-Widom laws for sparse random matrices The dimension-free structure of nonhomogeneous random matrices
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 38092677-2487-472b-9f0c-957e72beefd4 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Higher order fluctuations of extremal eigenvalues of sparse random matrices
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 66ef6070-23d4-437a-a0f9-333e3d34fc3f · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge universality for deformed Wigner matrices
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 75b5a787-7d4b-432e-b670-4a90b3a83b98 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Local law and Tracy-Widom limit for sparse random matrices
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 60521d36-5a7a-4c41-8ffd-75a981e51919 · outbound
Quantitative Tracy-Widom laws for sparse random matrices A necessary and sufficient condition for edge universality of Wigner matrices
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2642d67e-c139-45a8-b280-8d025017dc2b · outbound
Quantitative Tracy-Widom laws for sparse random matrices A goodness-of-fit test for stochastic block models
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e4b09439-ddc8-4c34-84b8-bcc8a57b6001 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Edge statistics for random band matrices
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 683cab5d-5957-4c9b-8b2d-c432b9a74a3f · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9760bbf4-f729-40ab-a480-858f481cbb58 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2606230b-4486-4203-9b13-ece1f702a76f · outbound
Quantitative Tracy-Widom laws for sparse random matrices Wigner random matrices with non-symmetrically distributed entries
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c858ebda-73c3-40b2-b74a-22a94462a754 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Convergence rate to the Tracy-Widom laws for the largest eigenvalue of Wigner matrices
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 61cd4e9d-d108-49cd-bca1-a26a5eab8100 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Quantitative Tracy-Widom laws for the largest eigenvalue of generalized Wigner matrices
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1704820a-c8d8-47e4-ba25-2fba7ef66018 · outbound
Quantitative Tracy-Widom laws for sparse random matrices The spectral edge of some random band matrices
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e7c1056c-3f05-4da8-9818-3710e63cf44c · outbound
Quantitative Tracy-Widom laws for sparse random matrices Universality at the edge of the spectrum in Wigner random matrices
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a6e144fc-f266-4908-8ea5-7439b6d2c6dc · outbound
Quantitative Tracy-Widom laws for sparse random matrices Random matrices: universality of local eigenvalue statistics up to the edge
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 79249518-9e02-4a44-aaf7-0f04fe4e1071 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Outliers in spectrum of sparse Wigner matrices
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 572efe1a-c97d-4e1d-9c04-6d2b03daefc3 · outbound
Quantitative Tracy-Widom laws for sparse random matrices Level-spacing distributions and the Airy kernel
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fe49556a-105d-4501-8da5-71288a164338 · outbound
Quantitative Tracy-Widom laws for sparse random matrices On orthogonal and symplectic matrix ensembles
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 44dca746-cca6-4d15-a24e-a8891125098d · outbound
Quantitative Tracy-Widom laws for sparse random matrices Spectral norm of random matrices
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation af475524-51be-43cf-9e35-5c64623fd01b · inbound
Order statistics for edge eigenvectors of Wigner matrices Quantitative Tracy-Widom laws for sparse random matrices
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.