{"paper":{"title":"Probing the large deviations for the Beta random walk in random medium","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR","nlin.SI"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alexander K. Hartmann, Alexandre Krajenbrink, Pierre Le Doussal","submitted_at":"2023-07-27T17:47:08Z","abstract_excerpt":"We consider a discrete-time random walk on a one-dimensional lattice with space and time-dependent random jump probabilities, known as the Beta random walk. We are interested in the probability that, for a given realization of the jump probabilities (a sample), a walker starting at the origin at time $t=0$ is at position beyond $\\xi \\sqrt{T/2}$ at time $T$. This probability fluctuates from sample to sample and we study the large-deviation rate function which characterizes the tails of its distribution at large time $T \\gg 1$. It is argued that, up to a simple rescaling, this rate function is i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.15041","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.15041/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}