{"paper":{"title":"Localization for a random walk in slowly decreasing random potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christophe Gallesco, Gunter M. Sch\\\"utz, Serguei Popov","submitted_at":"2012-10-06T15:43:34Z","abstract_excerpt":"We consider a continuous time random walk $X$ in random environment on $\\Z^+$ such that its potential can be approximated by the function $V: \\R^+\\to \\R$ given by $V(x)=\\sig W(x) -\\frac{b}{1-\\alf}x^{1-\\alf}$ where $\\sig W$ a Brownian motion with diffusion coefficient $\\sig>0$ and parameters $b$, $\\alf$ are such that $b>0$ and $0<\\alf<1/2$. We show that $\\P$-a.s.\\ (where $\\P$ is the averaged law) $\\lim_{t\\to \\infty} \\frac{X_t}{(C^*(\\ln\\ln t)^{-1}\\ln t)^{\\frac{1}{\\alf}}}=1$ with $C^*=\\frac{2\\alf b}{\\sig^2(1-2\\alf)}$. In fact, we prove that by showing that there is a trap located around $(C^*(\\ln"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1972","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"}