Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T05:17:35.452530Z
Paper Citation Record · LEDGER
Exact closed-form recurrence probabilities for biased random walks at any step number
As of 18 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2412.17994.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-11T05:17:35.401693Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-11T05:17:35.471788Z
Reference resolution
18 of 18 outbound references displayed
- verified exact1
- verified fuzzy13
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation cc9bcf91-bb07-4c88-9f6d-19b24ebbdb48 · outbound
This paper cites Exact closed-form recurrence probabilities for biased random walks at any step number.
Exact closed-form recurrence probabilities for biased random walks at any step number Exact closed-form recurrence probabilities for biased random walks at any step number
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T05:17:35.476467Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation f7a681f9-01b6-47f8-a52f-09ce4bdf9551 · outbound
This paper cites This is in agreement with the fact that return can occur only at even step numbers.
Exact closed-form recurrence probabilities for biased random walks at any step number This is in agreement with the fact that return can occur only at even step numbers
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.612210Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 4d6901e0-4de8-4ae9-8c2f-dab8cf49abb5 · outbound
This paper cites Ann., 84 (1921).
Exact closed-form recurrence probabilities for biased random walks at any step number Ann., 84 (1921)
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.604263Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation fb16ec22-3435-40ba-9c42-94d4dba7fb54 · outbound
This paper cites and Snell, J.L.
Exact closed-form recurrence probabilities for biased random walks at any step number and Snell, J.L
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.596226Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 83a56f9c-3461-44c2-bc8f-f5ab079cbe9d · outbound
This paper cites and Sokolov, I.M., First Steps in Random Walks: From Tools to Applications (Oxford University Press Inc., New York) 2011.
Exact closed-form recurrence probabilities for biased random walks at any step number and Sokolov, I.M., First Steps in Random Walks: From Tools to Applications (Oxford University Press Inc., New York) 2011
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.588486Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b88c8849-6c07-4fed-a4c5-8e2fbca28a5c · outbound
This paper cites an unresolved cited work.
Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:17:35.580932Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 3b6fb2e2-c4a1-40af-a53a-f815cb8df979 · outbound
This paper cites and Majumdar, S., Phys.
Exact closed-form recurrence probabilities for biased random walks at any step number and Majumdar, S., Phys
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.571685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 992b3bf5-56d5-4705-899e-5d259f7f770c · outbound
This paper cites and Wordeman, L., Curr.
Exact closed-form recurrence probabilities for biased random walks at any step number and Wordeman, L., Curr
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.563819Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 4a9b11a5-c73f-4f89-bc60-96e55cc94afb · outbound
This paper cites an unresolved cited work.
Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:17:35.554973Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 54fd8ae0-65f1-414d-bd56-9479f6f157bf · outbound
This paper cites Mag., 80 (2007) 5.
Exact closed-form recurrence probabilities for biased random walks at any step number Mag., 80 (2007) 5
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.546422Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 49e461b8-bd5c-47c0-a1ac-b4bcac50eb61 · outbound
This paper cites and Amir, A.
Exact closed-form recurrence probabilities for biased random walks at any step number and Amir, A
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.539316Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 0687aa99-cd95-4713-bcb9-1dbb739d83ac · outbound
This paper cites an unresolved cited work.
Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T05:17:35.435944Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0eca56c0-9411-423e-9b83-4b188f7933f3 · outbound
This paper cites and Stegun I.A., Handbook of Mathematical Functions with F ormulas, Graphs, and Mathematical Tables, 9th ed.
Exact closed-form recurrence probabilities for biased random walks at any step number and Stegun I.A., Handbook of Mathematical Functions with F ormulas, Graphs, and Mathematical Tables, 9th ed
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.527787Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 8c7d7430-de4a-45e5-bd89-ca49b9c111fd · outbound
This paper cites an unresolved cited work.
Exact closed-form recurrence probabilities for biased random walks at any step number Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:17:35.519327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation eca0fce2-7ae7-46c8-9328-f96b31d4eae2 · outbound
This paper cites and Vale, R.D., Curr.
Exact closed-form recurrence probabilities for biased random walks at any step number and Vale, R.D., Curr
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.510893Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 00ea272a-4ad8-4d96-b711-795e495e6561 · outbound
This paper cites and Grill, S.W., Phys.
Exact closed-form recurrence probabilities for biased random walks at any step number and Grill, S.W., Phys
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.502868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation a06741f9-74ad-4086-9718-314258a26ed7 · outbound
This paper cites and John, K., PRX Life, 1 (2023) 1.
Exact closed-form recurrence probabilities for biased random walks at any step number and John, K., PRX Life, 1 (2023) 1
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.494558Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 30907063-df47-4564-a22d-9c360b0783a0 · outbound
This paper cites and Vale, R.D.
Exact closed-form recurrence probabilities for biased random walks at any step number and Vale, R.D
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:17:35.485924Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Pith citing papers
Observation cc9bcf91-bb07-4c88-9f6d-19b24ebbdb48 · inbound
Exact closed-form recurrence probabilities for biased random walks at any step number cites this paper.
Exact closed-form recurrence probabilities for biased random walks at any step number Exact closed-form recurrence probabilities for biased random walks at any step number
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T05:17:35.476467Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.