Paper Citation Record · LEDGER

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$

As of 13 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2411.15724.

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

pith.paper-citation-record.v1
2411.15724 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T14:15:31.781889Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

28 of 28 outbound references displayed

verified exact0
verified fuzzy23
unresolved5
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External citation measurements

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Outbound references

Observation 19bb8133-5b27-4fc0-aeea-aa2dc540a641 · outbound

This paper cites Ambrosio, M.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Ambrosio, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:32.004530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5d5cb10f-358b-42b6-be9d-e4064479e360 · outbound

This paper cites Ambrosio, F.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Ambrosio, F

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.995997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e156fcfe-1a5e-4a11-b339-53b44dcf0b8a · outbound

This paper cites Bényi, T.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Bényi, T

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.988518Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation de991aff-72aa-480a-be0d-fac64683f826 · outbound

This paper cites Berkes, B.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Berkes, B

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.981060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c0a4eb43-1273-4114-bf23-c66ced83858b · outbound

This paper cites Berkes, B.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Berkes, B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.972785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8f41c294-9897-42f1-94b1-e227f2a8a18b · outbound

This paper cites Berkes, B.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Berkes, B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.964584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c9302a15-91f1-44a3-9eb8-b0f339c4932d · outbound

This paper cites an unresolved cited work.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:15:31.957714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7a9642f6-8551-4869-ae6d-cb0e536e9805 · outbound

This paper cites an unresolved cited work.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:15:31.949383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c08fe089-451c-4ea2-9dd4-1a09f7f98c18 · outbound

This paper cites Borda, Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric, Ann.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Borda, Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric, Ann

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.943310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 152852bb-dab8-4cb7-8511-c99263b71d6b · outbound

This paper cites Brown, S.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Brown, S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.937132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b3981648-6f41-4c67-8ebe-b477abadd092 · outbound

This paper cites Cassels, An Introduction to Diophantine Approximation , Cambridge University Press, Cambridge, 1957.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Cassels, An Introduction to Diophantine Approximation , Cambridge University Press, Cambridge, 1957

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.931463Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b3238db3-c0b9-42db-a564-aaf6a1a7e9ed · outbound

This paper cites Durrett, Probability–theory and examples , 5th edn.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Durrett, Probability–theory and examples , 5th edn

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.924465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0d934d43-2fd7-41d0-b9ec-bc1a38538aa5 · outbound

This paper cites Graham, Irregularity of distribution in Wasserstein distance.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Graham, Irregularity of distribution in Wasserstein distance

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.917200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8367534d-da54-4a0f-986b-238801dbd435 · outbound

This paper cites Huesmann, F.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Huesmann, F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.910493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9150312d-b97a-4bff-aa9a-1f8a4f3ae154 · outbound

This paper cites Kawata, Fourier Analysis in Probability Theory , Academic Press, 1972.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Kawata, Fourier Analysis in Probability Theory , Academic Press, 1972

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.903384Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 02b3a48b-ea91-4bb8-add1-a085dd27024c · outbound

This paper cites Kuipers, H.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Kuipers, H

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.895820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ebc42b07-988a-4cf9-9313-8894650937fe · outbound

This paper cites Ledoux, On optimal matching of Gaussian samples , Zap.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Ledoux, On optimal matching of Gaussian samples , Zap

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.888473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 20cf7634-d471-45e5-8a52-aca5708d64f3 · outbound

This paper cites Peyre, Comparison between W2 distance and ˙H −1 norm, and localization of Wasser- stein distance , ESAIM Control Optim.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Peyre, Comparison between W2 distance and ˙H −1 norm, and localization of Wasser- stein distance , ESAIM Control Optim

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.879946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a1ff7a90-90c1-4e93-8d84-d5799bbee086 · outbound

This paper cites Schatte, On the asymptotic uniform distribution of sums reduced mod 1 , Math.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Schatte, On the asymptotic uniform distribution of sums reduced mod 1 , Math

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.871926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a666e9f6-9d82-4081-83a2-ac86259a2074 · outbound

This paper cites Schmidt, Diophantine Approximations and Diophantine Equations , Lecture Notes in Mathematics 1467.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Schmidt, Diophantine Approximations and Diophantine Equations , Lecture Notes in Mathematics 1467

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.863499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 456b2650-4291-403c-afc1-4be53d044216 · outbound

This paper cites an unresolved cited work.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:15:31.855627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 188d25d6-4c11-49ad-9623-3957083a0587 · outbound

This paper cites an unresolved cited work.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:15:31.848127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0e0d0f18-2e47-43ed-930b-0554b91ea218 · outbound

This paper cites Villani, Topics in Optimal Transportation , Graduate Studies in Mathematics, vol.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Villani, Topics in Optimal Transportation , Graduate Studies in Mathematics, vol

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.841567Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d6590284-c755-4365-ac8b-402aee9c3f54 · outbound

This paper cites Wang, Convergence in Wasserstein distance for empirical measure s of Dirichlet diﬀusion processes on manifolds , J.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Wang, Convergence in Wasserstein distance for empirical measure s of Dirichlet diﬀusion processes on manifolds , J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.834037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 901ddac0-c6d0-445b-8142-70b2a2ef5784 · outbound

This paper cites an unresolved cited work.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:15:31.826452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3b5b23b3-8470-44ac-ba14-353dd80409f2 · outbound

This paper cites Wang, J.-X.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Wang, J.-X

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.819117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ea77f1d2-4748-455a-a552-51fa9441de9c · outbound

This paper cites Weber, Discrepancy of randomly sampled sequences of reals , Math.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Weber, Discrepancy of randomly sampled sequences of reals , Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.811703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f8f4e22f-cff0-462e-af02-d7b8218c2808 · outbound

This paper cites Weyl, Über die Gleichverteilung von Zahlen mod.

Wasserstein Convergence Rates for Empirical Measures of Random Subsequence of $\{n\alpha\}$ Weyl, Über die Gleichverteilung von Zahlen mod

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:15:31.803147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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