Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T20:31:29.028253Z
Paper Citation Record · LEDGER
The localization transition for the directed polymer in a random environment is smooth
As of 17 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 4 inbound Pith citation observations for arXiv:2505.13382.
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 2026-08-06T17:43:25.025867Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-01T20:06:12.290191Z
Reference resolution
40 of 40 outbound references displayed
- verified exact0
- verified fuzzy37
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 112a7b61-2ec1-4479-835b-f1c0645c3c6c · outbound
This paper cites The intermediate disorder regime for directed poly- mers in dimension 1 + 1.Ann.
The localization transition for the directed polymer in a random environment is smooth The intermediate disorder regime for directed poly- mers in dimension 1 + 1.Ann
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.918399Z
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 ea2f3fbe-70e2-4a0e-9db9-95f53f569bf5 · outbound
This paper cites The endpoint distribution of directed polymers.Ann.
The localization transition for the directed polymer in a random environment is smooth The endpoint distribution of directed polymers.Ann
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.891858Z
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 bd7bca1a-ca3f-4a7c-b5c2-13ca559d5ce1 · outbound
This paper cites The stochastic heat equation with multiplicative l´ evy noise: Existence, moments, and intermittency.Comm.
The localization transition for the directed polymer in a random environment is smooth The stochastic heat equation with multiplicative l´ evy noise: Existence, moments, and intermittency.Comm
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.870151Z
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 920350cf-51c2-4318-aa93-7c1a9172fb22 · outbound
This paper cites The high-temperature behavior for the directed polymer in dimension 1 + 2.Ann.
The localization transition for the directed polymer in a random environment is smooth The high-temperature behavior for the directed polymer in dimension 1 + 2.Ann
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.849433Z
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 2b49e849-0ef4-46b4-b349-1adaf3d110cd · outbound
This paper cites Toninelli.
The localization transition for the directed polymer in a random environment is smooth Toninelli
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.822939Z
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 f349b7b9-7156-411a-be79-e08aa83d061e · outbound
This paper cites A condition for weak disorder for directed polymers in random environment.Electron.
The localization transition for the directed polymer in a random environment is smooth A condition for weak disorder for directed polymers in random environment.Electron
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.793485Z
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 420576fb-3f7b-4bd1-b0f2-32fd833d3f20 · outbound
This paper cites Annealed vs quenched critical points for a random walk pinning model.
The localization transition for the directed polymer in a random environment is smooth Annealed vs quenched critical points for a random walk pinning model
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.771330Z
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 09fccb8f-a57e-4463-a040-a906b0cbbc43 · outbound
This paper cites A note on the diffusion of directed polymers in a random environment.Comm.
The localization transition for the directed polymer in a random environment is smooth A note on the diffusion of directed polymers in a random environment.Comm
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.747005Z
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 09f0d724-d6cd-4b41-8dc0-4097c6124f72 · outbound
This paper cites Directed polymers on trees: a martingale approach.J.
The localization transition for the directed polymer in a random environment is smooth Directed polymers on trees: a martingale approach.J
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.727290Z
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 7ff31b57-3a4e-4259-9e60-6eb43eea6378 · outbound
This paper cites Universality in marginally relevant disordered systems.Ann.
The localization transition for the directed polymer in a random environment is smooth Universality in marginally relevant disordered systems.Ann
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.704201Z
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 4fa94844-6129-46a8-aa6d-2c2411aeb7da · outbound
This paper cites The critical 2d stochastic heat flow.Invent.
The localization transition for the directed polymer in a random environment is smooth The critical 2d stochastic heat flow.Invent
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.683564Z
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 636917bd-ef5e-4e7d-9445-b0cce131cf8a · outbound
This paper cites On the partition function of a directed polymer in a Gaussian random environment.Probab.
The localization transition for the directed polymer in a random environment is smooth On the partition function of a directed polymer in a Gaussian random environment.Probab
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.666334Z
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 408f5c7d-7ac9-4898-a1c2-5760285b87ac · outbound
This paper cites Springer International Publishing, 2017.
The localization transition for the directed polymer in a random environment is smooth Springer International Publishing, 2017
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.650592Z
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 ba1fe1fd-2c49-46a8-bd84-70b1f2bee0bd · outbound
This paper cites Directed polymers in a random environment: path localization and strong disorder.Bernoulli, 9(4):705–723, 2003.
The localization transition for the directed polymer in a random environment is smooth Directed polymers in a random environment: path localization and strong disorder.Bernoulli, 9(4):705–723, 2003
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.633719Z
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 c4733181-c2e7-4064-979e-c4b6b1e4dee4 · outbound
This paper cites Majorizing multiplicative cascades for directed polymers in random media.ALEA Lat.
The localization transition for the directed polymer in a random environment is smooth Majorizing multiplicative cascades for directed polymers in random media.ALEA Lat
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.614199Z
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 bc38a507-1f7a-4350-994c-bd1aed5a1eab · outbound
This paper cites Directed polymers in random environment are diffusive at weak disorder.
The localization transition for the directed polymer in a random environment is smooth Directed polymers in random environment are diffusive at weak disorder
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.593146Z
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 17134288-140d-4d20-a7ab-15d87f1bc9e2 · outbound
This paper cites Cook and B.
The localization transition for the directed polymer in a random environment is smooth Cook and B
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.578400Z
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 f1d71a3b-2a79-4238-90cf-d023e7a77ae9 · outbound
This paper cites Derrida and O.
The localization transition for the directed polymer in a random environment is smooth Derrida and O
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.562250Z
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 602c2d50-7962-43d3-b864-fac7cf5981cb · outbound
This paper cites Improved bounds for the transition temperature of directed polymers in a finite- dimensional random medium.J.
The localization transition for the directed polymer in a random environment is smooth Improved bounds for the transition temperature of directed polymers in a finite- dimensional random medium.J
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.548230Z
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 82c12b70-e57a-48bf-965c-11b13b307a42 · outbound
This paper cites Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments.Electron.
The localization transition for the directed polymer in a random environment is smooth Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments.Electron
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.527919Z
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 cc57df70-e778-4053-a05d-b43e950d788e · outbound
This paper cites Imperial College Press, London, 2007.
The localization transition for the directed polymer in a random environment is smooth Imperial College Press, London, 2007
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.502586Z
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 0dd85dea-d0e3-41dc-a1a9-404a02787b4a · outbound
This paper cites Huse and Christopher L.
The localization transition for the directed polymer in a random environment is smooth Huse and Christopher L
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.483692Z
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 6d0d5d1b-070d-436b-b771-c2e5d4882b93 · outbound
This paper cites Imbrie and Thomas Spencer.
The localization transition for the directed polymer in a random environment is smooth Imbrie and Thomas Spencer
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.471036Z
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 11085ed3-3e05-4bc6-941f-3c6bcbee8d0c · outbound
This paper cites Local limit theorem for directed polymers beyond theL 2-phase.Journal of the European Mathematical Society (to appear).
The localization transition for the directed polymer in a random environment is smooth Local limit theorem for directed polymers beyond theL 2-phase.Journal of the European Mathematical Society (to appear)
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.452933Z
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 524b4296-d92a-447a-a5af-67d6361548fc · outbound
This paper cites New characterization of the weak disorder phase of directed polymers in bounded random environments.Comm.
The localization transition for the directed polymer in a random environment is smooth New characterization of the weak disorder phase of directed polymers in bounded random environments.Comm
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.437954Z
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 de2cdcb1-2241-4fff-a6ef-93e539b9baff · outbound
This paper cites Fluctuations of partition functions of directed polymers in weak disorder beyond the L2-phase.
The localization transition for the directed polymer in a random environment is smooth Fluctuations of partition functions of directed polymers in weak disorder beyond the L2-phase
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.417962Z
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 357cd715-5bfe-424f-9230-3f2d3d0b806f · outbound
This paper cites Strong disorder and very strong disorder are equivalent for directed poly- mers.arXiv e-prints, page arXiv:2402.02562, February 2024.
The localization transition for the directed polymer in a random environment is smooth Strong disorder and very strong disorder are equivalent for directed poly- mers.arXiv e-prints, page arXiv:2402.02562, February 2024
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:31:28.968375Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c07295de-d008-4136-a1ad-d330b0d2e92b · outbound
This paper cites Coincidence of critical points for directed polymers for general environments and random walks.
The localization transition for the directed polymer in a random environment is smooth Coincidence of critical points for directed polymers for general environments and random walks
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T20:31:28.972997Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation adfc9880-11d6-4c69-a1dd-b2453a20258d · outbound
This paper cites The tail distribution of the partition function for directed polymers in the weak disorder phase.Comm.
The localization transition for the directed polymer in a random environment is smooth The tail distribution of the partition function for directed polymers in the weak disorder phase.Comm
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.389922Z
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 553f2bf9-66ef-40af-a764-4a99010184c3 · outbound
This paper cites Scaling of directed polymers in random media.Phys.
The localization transition for the directed polymer in a random environment is smooth Scaling of directed polymers in random media.Phys
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.373904Z
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 b8e11e4b-5680-4c02-aaae-95e10168e53a · outbound
This paper cites an unresolved cited work.
The localization transition for the directed polymer in a random environment is smooth Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T20:31:29.356242Z
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 d73f80be-cc4a-4137-a8eb-801a012058a8 · outbound
This paper cites New bounds for the free energy of directed polymers in dimension 1 + 1 and 1 + 2.Comm.
The localization transition for the directed polymer in a random environment is smooth New bounds for the free energy of directed polymers in dimension 1 + 1 and 1 + 2.Comm
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.339065Z
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 af2f7753-db5f-45c7-9deb-b25e948e0a57 · outbound
This paper cites A short proof of diffusivity for the directed polymers in the weak disorder phase.Electron.
The localization transition for the directed polymer in a random environment is smooth A short proof of diffusivity for the directed polymers in the weak disorder phase.Electron
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.315898Z
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 2a3a3827-eb5f-49fa-a2f0-65e6ec46d88d · outbound
This paper cites Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment.Stochastic Process.
The localization transition for the directed polymer in a random environment is smooth Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment.Stochastic Process
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.290573Z
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 a79308cd-4f5b-4df7-bdae-9c54ef6e4953 · outbound
This paper cites Freezing transition of the directed polymer in a 1+ d random medium: Location of the critical temperature and unusual critical properties.Phys.
The localization transition for the directed polymer in a random environment is smooth Freezing transition of the directed polymer in a 1+ d random medium: Location of the critical temperature and unusual critical properties.Phys
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.274057Z
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 737a3a7f-97d1-4826-82b2-ca3ecaa05cdc · outbound
This paper cites Numerical study of the directed polymer in a 1+ 3 dimensional random medium.The European Physical Journal B, 53(1):39–45, 2006.
The localization transition for the directed polymer in a random environment is smooth Numerical study of the directed polymer in a 1+ 3 dimensional random medium.The European Physical Journal B, 53(1):39–45, 2006
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.253494Z
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 e3613162-9d13-4b7e-bbcd-263a6c944898 · outbound
This paper cites Free energy of directed polymers in random environment in 1 + 1-dimension at high temperature.Electron.
The localization transition for the directed polymer in a random environment is smooth Free energy of directed polymers in random environment in 1 + 1-dimension at high temperature.Electron
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.237256Z
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 b94a781b-9e27-409e-b1f7-906aab83f653 · outbound
This paper cites Springer Science & Business Media, 2007.
The localization transition for the directed polymer in a random environment is smooth Springer Science & Business Media, 2007
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.220650Z
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 a7278af0-08c5-43e8-a2df-ac0ab131c0e3 · outbound
This paper cites Concentration inequalities for disordered models.ALEA Lat.
The localization transition for the directed polymer in a random environment is smooth Concentration inequalities for disordered models.ALEA Lat
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.202666Z
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 4d9907c1-f845-437b-a29d-2f949bd7108e · outbound
This paper cites Directed polymers in a random environment: a review of the phase transitions.Stochastic Process.
The localization transition for the directed polymer in a random environment is smooth Directed polymers in a random environment: a review of the phase transitions.Stochastic Process
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T20:31:29.178565Z
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 9335e711-8527-4daf-b57c-d05abe5585c5 · inbound
Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow cites this paper.
Enhanced noise sensitivity, 2D directed polymers and Stochastic Heat Flow The localization transition for the directed polymer in a random environment is smooth
Reference 39
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T17:43:25.025867Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 05f7cfd6-1e49-444d-9608-c51625a733ff · inbound
Dimers with layered disorder cites this paper.
Dimers with layered disorder The localization transition for the directed polymer in a random environment is smooth
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T17:12:41.527383Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a65dc93f-c7ca-4508-9893-64b093be4794 · inbound
Sharp behavior of the free energy for the two-dimensional directed polymer model cites this paper.
Sharp behavior of the free energy for the two-dimensional directed polymer model The localization transition for the directed polymer in a random environment is smooth
Reference 27
- Resolution
- verified exact
- arxiv_id, observed 2026-07-01T20:06:12.291429Z
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 56a83083-0dd1-467a-9d73-2cba19d0800e · inbound
Random walks in Dirichlet random environment in dimension $d+1$ cites this paper.
Random walks in Dirichlet random environment in dimension $d+1$ The localization transition for the directed polymer in a random environment is smooth
Reference 57
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T10:25:17.794478Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.