{"paper":{"title":"Moments of exit times from wedges for non-homogeneous random walks with asymptotically zero drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew R. Wade, Iain M. MacPhee, Mikhail V. Menshikov","submitted_at":"2008-06-27T16:38:41Z","abstract_excerpt":"We study quantitative asymptotics of planar random walks that are spatially non-homogeneous but whose mean drifts have some regularity. Specifically, we study the first exit time $\\tau_\\alpha$ from a wedge with apex at the origin and interior half-angle $\\alpha$ by a non-homogeneous random walk on the square lattice with mean drift at $x$ of magnitude $O(1/|x|)$ as $|x| \\to \\infty$. This is the critical regime for the asymptotic behaviour: under mild conditions, a previous result of the authors (see arXiv:0910.1772) stated that $\\tau_\\alpha < \\infty$ a.s. for any $\\alpha$ (while for a stronger"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.4561","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"}