{"paper":{"title":"The supremum of Brownian local times on Holder curves","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Burdzy, Richard Bass","submitted_at":"2000-02-01T19:12:19Z","abstract_excerpt":"For $f: [0,1]\\to \\R$, we consider $L^f_t$, the local time of space-time Brownian motion on the curve $f$. Let $\\sS_\\al$ be the class of all functions whose H\\\"older norm of order $\\al$ is less than or equal to 1. We show that the supremum of $L^f_1$ over $f$ in $\\sS_\\al$ is finite is $\\al>\\frac12$ and infinite if $\\al<\\frac12$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0002012","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"}