Paper Citation Record · LEDGER

Limiting spectral laws for sparse random circulant matrices

As of 20 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 1 inbound Pith citation observation for arXiv:2504.13833.

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

pith.paper-citation-record.v1
2504.13833 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:08:34.811086Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T16:34:45.852421Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T08:40:58.087141Z

Reference resolution

48 of 48 outbound references displayed

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External citation measurements

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Outbound references

Observation 8c0bfe59-0bdc-494e-a62a-7868c80522ee · outbound

This paper cites Random non-Abelian G-circulant matrices.

Limiting spectral laws for sparse random circulant matrices Random non-Abelian G-circulant matrices

Reference 1

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Observation 5b83b3fc-3d9e-491c-9c8b-a8f564392688 · outbound

This paper cites Random Cayley graphs and ex panders.

Limiting spectral laws for sparse random circulant matrices Random Cayley graphs and ex panders

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:38.054134Z

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Observation c2bafa48-7d07-4db8-b9ba-96a3c458b5cc · outbound

This paper cites The diameter of a ran dom Cayley graph of Zq.

Limiting spectral laws for sparse random circulant matrices The diameter of a ran dom Cayley graph of Zq

Reference 3

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Observation 7be9d2a6-b6ac-4bc9-8a3f-28a5f8b2160b · outbound

This paper cites Patterned sparse ran dom matrices: a moment approach.

Limiting spectral laws for sparse random circulant matrices Patterned sparse ran dom matrices: a moment approach

Reference 4

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Observation 95027e76-66ea-4af9-90e2-ec510d30075a · outbound

This paper cites Small sums of ﬁve roots of unity.

Limiting spectral laws for sparse random circulant matrices Small sums of ﬁve roots of unity

Reference 5

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Observation 5131b48c-21e0-4824-bc44-45cd2f66a359 · outbound

This paper cites Salem-Zygmund ineq uality for locally sub-Gaussian random variables, random trigonometric polynomials, and r andom circulant matrices.

Limiting spectral laws for sparse random circulant matrices Salem-Zygmund ineq uality for locally sub-Gaussian random variables, random trigonometric polynomials, and r andom circulant matrices

Reference 6

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Observation 16ae7f51-c021-4096-bed0-df63606f56bf · outbound

This paper cites Around the circula r law.

Limiting spectral laws for sparse random circulant matrices Around the circula r law

Reference 7

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Observation cefe75f7-01dc-4a2d-bf7b-c946c91b08f6 · outbound

This paper cites Limiting spectral distribution of XX 1 ma- trices.

Limiting spectral laws for sparse random circulant matrices Limiting spectral distribution of XX 1 ma- trices

Reference 8

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Observation 1f47e0fb-f66d-4558-82da-cd6be12b63cd · outbound

This paper cites Spectra l norm of circulant-type matrices.

Limiting spectral laws for sparse random circulant matrices Spectra l norm of circulant-type matrices

Reference 9

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Observation 6ba3facc-9444-4766-8202-1bd9710aff6e · outbound

This paper cites Limiting spectral distribu tion of a special circulant.

Limiting spectral laws for sparse random circulant matrices Limiting spectral distribu tion of a special circulant

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.424409Z

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Observation 0829f18f-3e50-40db-8e54-14afcb31bedc · outbound

This paper cites Random circulant matrices.

Limiting spectral laws for sparse random circulant matrices Random circulant matrices

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.354442Z

Source-reported events for the cited work

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Observation decd1502-43e9-4139-ad31-f28d698c196a · outbound

This paper cites Another look at the moment metho d for large dimensional random matrices.

Limiting spectral laws for sparse random circulant matrices Another look at the moment metho d for large dimensional random matrices

Reference 12

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Source-reported events for the cited work

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Observation 2bc9d725-027c-4a9d-9638-fd12f81e8b4c · outbound

This paper cites Patter ned random matrices and method of moments.

Limiting spectral laws for sparse random circulant matrices Patter ned random matrices and method of moments

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.286535Z

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Observation 8cc91232-86b7-4372-8ffe-db85a0e730bf · outbound

This paper cites Uniform expansion boun ds for Cayley graphs of SL2pFpq.

Limiting spectral laws for sparse random circulant matrices Uniform expansion boun ds for Cayley graphs of SL2pFpq

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.242284Z

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Observation 9f40c011-6592-4ebb-8dc5-982de0551d67 · outbound

This paper cites Spect ral measure of large random Hankel, Markov and Toeplitz matrices.

Limiting spectral laws for sparse random circulant matrices Spect ral measure of large random Hankel, Markov and Toeplitz matrices

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.171631Z

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Observation f8d0beb0-de07-4f5f-92f7-8e5abe0b57f6 · outbound

This paper cites On the independence number of sparser random Cayley graphs.

Limiting spectral laws for sparse random circulant matrices On the independence number of sparser random Cayley graphs

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.127405Z

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Observation 178256b4-b282-4489-a365-ce43936c0d72 · outbound

This paper cites Around the circular law: an update.

Limiting spectral laws for sparse random circulant matrices Around the circular law: an update

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:37.067240Z

Source-reported events for the cited work

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Observation df0b2876-d956-4e72-8abe-b802c41027d0 · outbound

This paper cites The threshol ds for diameter 2 in random Cayley graphs.

Limiting spectral laws for sparse random circulant matrices The threshol ds for diameter 2 in random Cayley graphs

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.979355Z

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Observation 631d5750-279e-4825-90ef-eae64e4ca250 · outbound

This paper cites On the clique number of random Cayley graphs and related topics.

Limiting spectral laws for sparse random circulant matrices On the clique number of random Cayley graphs and related topics

Reference 19

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Observation d0bb084f-ac53-4e73-bbd8-b5f91821ba52 · outbound

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

Limiting spectral laws for sparse random circulant matrices Group representations in probability and statistics , volume 11 of Institute of Mathematical Statistics Lecture Notes—Monograph Series

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.909109Z

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Observation fe50ed8e-49bd-4951-9ca6-d4154c4a1d5c · outbound

This paper cites Babai’s conjecture f or high-rank classical groups with random generators.

Limiting spectral laws for sparse random circulant matrices Babai’s conjecture f or high-rank classical groups with random generators

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.847183Z

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Observation 9788b94a-0de3-4f8e-af36-b4b3bb7d813a · outbound

This paper cites Random circulant d eterminants.

Limiting spectral laws for sparse random circulant matrices Random circulant d eterminants

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.784390Z

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Observation b4bc68f0-6ea8-49ee-b3b4-0895038c4d9e · outbound

This paper cites Proof methods in r andom matrix theory.

Limiting spectral laws for sparse random circulant matrices Proof methods in r andom matrix theory

Reference 23

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Observation 7b669018-3afa-41d9-ba87-571c4df1e279 · outbound

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Limiting spectral laws for sparse random circulant matrices Unresolved cited work

Reference 24

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Observation 7b9885fc-4bcd-440f-a85d-e449b8290e1e · outbound

This paper cites Classical Fourier analysis , volume 249 of Graduate Texts in Mathematics.

Limiting spectral laws for sparse random circulant matrices Classical Fourier analysis , volume 249 of Graduate Texts in Mathematics

Reference 25

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Observation 9e6f132a-0a1b-4494-b9d2-41fec427c94b · outbound

This paper cites Some applications of harmonic analysis to ar ithmetic combinatorics.

Limiting spectral laws for sparse random circulant matrices Some applications of harmonic analysis to ar ithmetic combinatorics

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.602957Z

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Observation 6a00ff25-bc36-45b3-9448-5ebaf177e057 · outbound

This paper cites Counting sets with small sumset, and the cliq ue number of random Cayley graphs.

Limiting spectral laws for sparse random circulant matrices Counting sets with small sumset, and the cliq ue number of random Cayley graphs

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.589587Z

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Observation b808c3d6-8aaa-4fbc-9f33-f134368fd505 · outbound

This paper cites On the chromatic number of random Cayley grap hs.

Limiting spectral laws for sparse random circulant matrices On the chromatic number of random Cayley grap hs

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.498069Z

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Observation d8e4407b-0b04-4bbe-80c8-2f428f019346 · outbound

This paper cites 100 open problems.

Limiting spectral laws for sparse random circulant matrices 100 open problems

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.418138Z

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Observation f13c74a9-6b84-4f40-b284-d5a998240488 · outbound

This paper cites Helfgott, Ákos Seress, and Andrzej Zuk.

Limiting spectral laws for sparse random circulant matrices Helfgott, Ákos Seress, and Andrzej Zuk

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.276224Z

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Observation 33f7ad30-bd50-4d3b-be8e-00d7b1770b90 · outbound

This paper cites Basic algebra.

Limiting spectral laws for sparse random circulant matrices Basic algebra

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.211478Z

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Observation cd4808af-6138-45f8-ba8b-d3f50234da8d · outbound

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Limiting spectral laws for sparse random circulant matrices Unresolved cited work

Reference 32

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Observation ff28ca4f-65b7-4943-ace7-31ea6cf70a05 · outbound

This paper cites Norms of randomiz ed circulant matrices.

Limiting spectral laws for sparse random circulant matrices Norms of randomiz ed circulant matrices

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.138575Z

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Observation dfc8e576-8338-41e2-9cab-26ea2a51608e · outbound

This paper cites Diameters of r andom circulant graphs.

Limiting spectral laws for sparse random circulant matrices Diameters of r andom circulant graphs

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:36.083335Z

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Observation eb06bc67-9377-4c17-ba17-2b859e4358d2 · outbound

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Limiting spectral laws for sparse random circulant matrices Unresolved cited work

Reference 35

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Limiting spectral laws for sparse random circulant matrices Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:08:35.967135Z

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Observation 9a1c5728-33a1-4bbd-80dc-c3311e377576 · outbound

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Limiting spectral laws for sparse random circulant matrices Unresolved cited work

Reference 37

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Observation ca463979-9460-45b8-a281-70cf137a5c1b · outbound

This paper cites Ein Beitrag zur analytischen Zahlenthe orie.

Limiting spectral laws for sparse random circulant matrices Ein Beitrag zur analytischen Zahlenthe orie

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.796201Z

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Observation b0a3ee93-8068-47f7-9540-c46dd222eaf8 · outbound

This paper cites One-point concentration of the clique a nd chromatic numbers of the random Cayley graph on Fn 2.

Limiting spectral laws for sparse random circulant matrices One-point concentration of the clique a nd chromatic numbers of the random Cayley graph on Fn 2

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.721739Z

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Observation 992cf0eb-a93f-46e4-9bb8-d42965bf3604 · outbound

This paper cites Unsolved Problems: How Small Can a Sum o f Roots of Unity Be? Amer.

Limiting spectral laws for sparse random circulant matrices Unsolved Problems: How Small Can a Sum o f Roots of Unity Be? Amer

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.679582Z

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Observation f9c0e9b6-b0a9-4554-a0e8-2061493839d2 · outbound

This paper cites The limiting spectral law for sparse iid matrices.

Limiting spectral laws for sparse random circulant matrices The limiting spectral law for sparse iid matrices

Reference 41

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Source-reported events for the cited work

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This paper cites How small can a sum of a few roots of unity be? https://mathoverflow.net/questions/46068/how-small- can-a-sum-of-a-few-roots-of-unity-be.

Limiting spectral laws for sparse random circulant matrices How small can a sum of a few roots of unity be? https://mathoverflow.net/questions/46068/how-small- can-a-sum-of-a-few-roots-of-unity-be

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.476682Z

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Observation 1b26ab63-7383-4e5c-a2ae-26a0081202c8 · outbound

This paper cites Topics in random matrix theory , volume 132 of Graduate Studies in Mathematics.

Limiting spectral laws for sparse random circulant matrices Topics in random matrix theory , volume 132 of Graduate Studies in Mathematics

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.463655Z

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Observation f6e92ea0-0a4e-4616-ae60-6958eb22b832 · outbound

This paper cites Additive combinatorics, volume 105 of Cambridge Studies in Advanced Mathematics.

Limiting spectral laws for sparse random circulant matrices Additive combinatorics, volume 105 of Cambridge Studies in Advanced Mathematics

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.307832Z

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Observation 55063c74-78f8-415e-ac29-5a7df96cd878 · outbound

This paper cites Random matrices: the circular la w.

Limiting spectral laws for sparse random circulant matrices Random matrices: the circular la w

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.145647Z

Source-reported events for the cited work

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Observation c1312046-f151-4702-98f0-bc7d8a397b03 · outbound

This paper cites Random matrices: universality o f ESDs and the circular law.

Limiting spectral laws for sparse random circulant matrices Random matrices: universality o f ESDs and the circular law

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T12:08:35.024632Z

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Observation da9e4a55-cb59-4ccd-a352-e727b68e08aa · outbound

This paper cites Quantitative invertibility of non-Hermitian random matrices.

Limiting spectral laws for sparse random circulant matrices Quantitative invertibility of non-Hermitian random matrices

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-16T12:08:34.805664Z

Source-reported events for the cited work

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Observation 57655a9e-7fd9-44ca-86fa-f974a3b5541a · outbound

This paper cites an unresolved cited work.

Limiting spectral laws for sparse random circulant matrices Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-16T12:08:34.964830Z

Source-reported events for the cited work

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Pith citing papers

Observation 219b89a2-5c4a-4c6f-a056-9c33df4d4947 · inbound

Least singular values of shifted sparse random combinatorial matrices cites this paper.

Least singular values of shifted sparse random combinatorial matrices Limiting spectral laws for sparse random circulant matrices

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T08:40:58.091800Z

Source-reported events for the cited work

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