{"paper":{"title":"Differing averaged and quenched large deviations for random walks in random environments in dimensions two and three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Atilla Yilmaz, Ofer Zeitouni","submitted_at":"2009-10-07T06:53:47Z","abstract_excerpt":"We consider the quenched and the averaged (or annealed) large deviation rate functions $I_q$ and $I_a$ for space-time and (the usual) space-only RWRE on $\\mathbb{Z}^d$. By Jensen's inequality, $I_a\\leq I_q$. In the space-time case, when $d\\geq3+1$, $I_q$ and $I_a$ are known to be equal on an open set containing the typical velocity $\\xi_o$. When $d=1+1$, we prove that $I_q$ and $I_a$ are equal only at $\\xi_o$. Similarly, when d=2+1, we show that $I_a<I_q$ on a punctured neighborhood of $\\xi_o$. In the space-only case, we provide a class of non-nestling walks on $\\mathbb{Z}^d$ with d=2 or 3, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1169","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"}