{"paper":{"title":"Hitting Probabilities of a Brownian flow with Radial Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carl Mueller, Eyal Neuman, Jong Jun Lee","submitted_at":"2018-02-16T16:15:34Z","abstract_excerpt":"We consider a stochastic flow $\\phi_t(x,\\omega)$ in $\\mathbb{R}^n$ with initial point $\\phi_0(x,\\omega)=x$, driven by a single $n$-dimensional Brownian motion, and with an outward radial drift of magnitude $\\frac{ F(\\|\\phi_t(x)\\|)}{\\|\\phi_t(x)\\|}$, with $F$ nonnegative, bounded and Lipschitz. We consider initial points $x$ lying in a set of positive distance from the origin. We show that there exist constants $C^*,c^*>0$ not depending on $n$, such that if $F>C^*n$ then the image of the initial set under the flow has probability 0 of hitting the origin. If $0\\leq F \\leq c^*n^{3/4}$, and if the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06010","kind":"arxiv","version":3},"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"}