{"paper":{"title":"Localization and number of visited valleys for a transient diffusion in random environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexis Devulder (LM-Versailles), Pierre Andreoletti (MAPMO)","submitted_at":"2013-11-25T15:22:40Z","abstract_excerpt":"We consider a transient diffusion in a $(-\\kappa/2)$-drifted Brownian potential $W\\_{\\kappa}$ with $0\\textless{}\\kappa\\textless{}1$.\nWe prove its localization at time $t$ in the neighborhood of some random points depending only on the environment, which are the positive $h\\_t$-minima of the environment, for $h\\_t$ a bit smaller than $\\log t$.\nWe also prove an Aging phenomenon for the diffusion, a renewal theorem for the hitting time of the farthest visited valley, and provide a  central limit theorem for the number of valleys  visited up to time $t$.\nThe proof relies on a decomposition of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6332","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"}