{"paper":{"title":"Oscillations of quenched slowdown asymptotics for ballistic one-dimensional random walk in a random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson, Sung Won Ahn","submitted_at":"2015-09-01T19:08:03Z","abstract_excerpt":"We consider a one dimensional random walk in a random environment (RWRE) with a positive speed $\\lim_{n\\to\\infty}\\frac{X_n}{n}=v_\\alpha>0$. Gantert and Zeitouni showed that if the environment has both positive and negative local drifts then the quenched slowdown probabilities $P_\\omega(X_n < xn)$ with $x \\in (0,v_\\alpha)$ decay approximately like $\\exp\\{-n^{1-1/s}\\}$ for a deterministic $s > 1$. More precisely, they showed that $n^{-\\gamma} \\log P_\\omega( X_n < x n)$ converges to $0$ or $-\\infty$ depending on whether $\\gamma > 1-1/s$ or $\\gamma < 1-1/s$. In this paper, we improve on this by sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00445","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":""},"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"}