{"paper":{"title":"On the most visited sites of planar Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Peter M\\\"orters, Valentina Cammarota","submitted_at":"2012-02-08T22:14:49Z","abstract_excerpt":"Let (B_t : t > 0) be a planar Brownian motion and define gauge functions $\\phi_\\alpha(s)=log(1/s)^{-\\alpha}$ for $\\alpha>0$. If $\\alpha<1$ we show that almost surely there exists a point x in the plane such that $H^{\\phi_\\alpha}({t > 0 : B_t=x})>0$, but if $\\alpha>1$ almost surely $H^{\\phi_\\alpha} ({t > 0 : B_t=x})=0$ simultaneously for all $x\\in R^2$. This resolves a longstanding open problem posed by S.,J. Taylor in 1986."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1847","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"}