{"paper":{"title":"Quenched limits for transient, zero speed one-dimensional random walk in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson, Ofer Zeitouni","submitted_at":"2007-04-13T15:12:46Z","abstract_excerpt":"We consider a nearest-neighbor, one dimensional random walk $\\{X_n\\}_{n\\geq0}$ in a random i.i.d. environment, in the regime where the walk is transient but with zero speed, so that $X_n$ is of order $n^s$ for some $s<1$. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: There exist sequences $\\{n_k\\}$ and $\\{x_k\\}$ depending on the environment only, such that $X_{n_k}-x_k=o(\\log n_k)^2$ (a localized regime). On the other hand, there exist sequences $\\{t_m\\}$ and $\\{s_m\\}$ depending on the environment only, such that $\\log s_m/\\log t_m\\to s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.1778","kind":"arxiv","version":2},"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"}