Paper Citation Record · LEDGER

Localization of eigenfunctions in amenable unimodular random networks

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2606.17187.

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

pith.paper-citation-record.v1
2606.17187 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T02:26:48.089675Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

18 of 18 outbound references displayed

verified exact2
verified fuzzy0
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 87dc9e98-bc6d-4b43-96ad-2b635dee8a1e · outbound

This paper cites Benjamini- Schramm convergence and pointwise convergence of the spectral measure.

Localization of eigenfunctions in amenable unimodular random networks Benjamini- Schramm convergence and pointwise convergence of the spectral measure

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

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Observation a9607605-0a71-4b6d-91ad-50f00ca0e5e5 · outbound

This paper cites Processes on Unimodular Random Net- works.Electronic Journal of Probability, 12:1454 – 1508, 2007.

Localization of eigenfunctions in amenable unimodular random networks Processes on Unimodular Random Net- works.Electronic Journal of Probability, 12:1454 – 1508, 2007

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

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Observation 531de442-b5d7-4ce3-9909-3361c4c161a8 · outbound

This paper cites 12 pages.

Localization of eigenfunctions in amenable unimodular random networks 12 pages

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

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Observation ed245e7c-6969-4747-a534-21b894711686 · outbound

This paper cites On a family of Schreier graphs of interme- diate growth associated with a self-similar group.European Journal of Combinatorics, 33(7):1408–1421, 2012.

Localization of eigenfunctions in amenable unimodular random networks On a family of Schreier graphs of interme- diate growth associated with a self-similar group.European Journal of Combinatorics, 33(7):1408–1421, 2012

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5eaf179c-a758-448e-8d77-8b57ff406446 · outbound

This paper cites Spectrum of random graphs.

Localization of eigenfunctions in amenable unimodular random networks Spectrum of random graphs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

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Observation 0bb6b91f-a667-4922-80b5-714a3570f9b3 · outbound

This paper cites Sparse graphs and their Benjamini-Schramm limits: a spectral tour.arXiv preprint arXiv:2510.10299, 2025.

Localization of eigenfunctions in amenable unimodular random networks Sparse graphs and their Benjamini-Schramm limits: a spectral tour.arXiv preprint arXiv:2510.10299, 2025

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-07-03T18:38:50.028748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 00aeb05f-eefe-4bff-8266-7d178da149cf · outbound

This paper cites Spectral properties of graphs associated to the Basilica group.International Mathematics Research Notices, 2026(5):rnag037, 2026.

Localization of eigenfunctions in amenable unimodular random networks Spectral properties of graphs associated to the Basilica group.International Mathematics Research Notices, 2026(5):rnag037, 2026

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b3acba5-d65b-4a5e-a937-f31bd3bd02d4 · outbound

This paper cites On the analytic zero divisor conjecture of Linnell.Bulletin of the London Mathematical Society, 35(2):236–238, 2003.

Localization of eigenfunctions in amenable unimodular random networks On the analytic zero divisor conjecture of Linnell.Bulletin of the London Mathematical Society, 35(2):236–238, 2003

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83b57896-9130-411f-bb60-05d5cb2f2908 · outbound

This paper cites On spectra and spectral measures of Schreier and Cayley graphs.International Mathematics Research Notices, 2022(15):11957–12002, 2022.

Localization of eigenfunctions in amenable unimodular random networks On spectra and spectral measures of Schreier and Cayley graphs.International Mathematics Research Notices, 2022(15):11957–12002, 2022

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d8621af-98e2-4ba0-979b-55ab93463fa6 · outbound

This paper cites Laplace and Schrödinger operators without eigenvalues on homogeneous amenable graphs.The Asian Journal of Mathematics, 2023.

Localization of eigenfunctions in amenable unimodular random networks Laplace and Schrödinger operators without eigenvalues on homogeneous amenable graphs.The Asian Journal of Mathematics, 2023

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a52e0bbc-c93b-43e0-8fa0-a051f1561efb · outbound

This paper cites The lamplighter group as a group generated by a 2-state automaton, and its spectrum.Geometriae Dedicata, 87(1):209–244, 2001.

Localization of eigenfunctions in amenable unimodular random networks The lamplighter group as a group generated by a 2-state automaton, and its spectrum.Geometriae Dedicata, 87(1):209–244, 2001

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6a9e9a5-0b00-44ba-b68b-bfca65d9a538 · outbound

This paper cites The base change in the Atiyah and the Lück approximation conjectures.Geometric and Functional Analysis, 29(2):464– 538, 2019.

Localization of eigenfunctions in amenable unimodular random networks The base change in the Atiyah and the Lück approximation conjectures.Geometric and Functional Analysis, 29(2):464– 538, 2019

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 809c1697-c1d2-42b1-a62d-56f2c6ed7b9c · outbound

This paper cites Amenability, hyperfiniteness, and isoperimetric in- equalities.Comptes Rendus de l’Académie des Sciences de Paris, Série I Mathématique, 325:999–1004, 1997.

Localization of eigenfunctions in amenable unimodular random networks Amenability, hyperfiniteness, and isoperimetric in- equalities.Comptes Rendus de l’Académie des Sciences de Paris, Série I Mathématique, 325:999–1004, 1997

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 045d5686-6e3f-432d-8666-3f55ec70ec8e · outbound

This paper cites Hausdorff dimension of the harmonic measure on trees.

Localization of eigenfunctions in amenable unimodular random networks Hausdorff dimension of the harmonic measure on trees

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0bca33b-3bb4-4c1c-81ab-5468e4fb488d · outbound

This paper cites On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$.

Localization of eigenfunctions in amenable unimodular random networks On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-07-03T18:38:50.025826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 649d890c-2741-4790-b747-754819041ed3 · outbound

This paper cites Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence.Mathematische Zeitschrift, 263(4):813–835, 2009.

Localization of eigenfunctions in amenable unimodular random networks Hamiltonians on discrete structures: jumps of the integrated density of states and uniform convergence.Mathematische Zeitschrift, 263(4):813–835, 2009

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7db8778b-b5dc-42e7-921c-cc46b0adf689 · outbound

This paper cites Spectral analysis on infinite Sierpiński gaskets.Journal of Functional Analysis, 159(2):537–567, 1998.

Localization of eigenfunctions in amenable unimodular random networks Spectral analysis on infinite Sierpiński gaskets.Journal of Functional Analysis, 159(2):537–567, 1998

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26638199-ab89-4be3-843e-23f2d8a1d5fc · outbound

This paper cites Sofic groups and diophantine approximation.Communica- tions on Pure and Applied Mathematics, 61(8):1155–1171, 2008.

Localization of eigenfunctions in amenable unimodular random networks Sofic groups and diophantine approximation.Communica- tions on Pure and Applied Mathematics, 61(8):1155–1171, 2008

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-27T02:26:48.089675Z

Source-reported events for the cited work

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Pith citing papers

No inbound Pith citation observations are available.