{"paper":{"title":"Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xia Chen","submitted_at":"2012-07-27T08:13:43Z","abstract_excerpt":"Let $B_s$ be a $d$-dimensional Brownian motion and $\\omega(dx)$ be an independent Poisson field on $\\mathbb{R}^d$. The almost sure asymptotics for the logarithmic moment generating function [\\log\\math bb{E}_0\\exp\\biggl{\\pm\\theta\\int_0^t\\bar{V}(B_s) ds\\biggr}\\qquad (t\\to\\infty)] are investigated in connection with the renormalized Poisson potential of the form [\\bar{V}(x)=\\int_{\\mathbb{R}^d}{\\frac{1}{|y-x|^p}}[\\omega(dy)-dy],\\qquad x\\in\\mathbb{R}^d.] The investigation is motivated by some practical problems arising from the models of Brownian motion in random media and from the parabolic Anders"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6483","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"}