{"paper":{"title":"Brownian motion with variable drift: 0-1 laws, hitting probabilities and Hausdorff dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Perla Sousi, Yuval Peres","submitted_at":"2010-10-14T17:33:58Z","abstract_excerpt":"By the Cameron--Martin theorem, if a function $f$ is in the Dirichlet space $D$, then $B+f$ has the same a.s. properties as standard Brownian motion, $B$. In this paper we examine properties of $B+f$ when $f \\notin D$. We start by establishing a general 0-1 law, which in particular implies that for any fixed $f$, the Hausdorff dimension of the image and the graph of $B+f$ are constants a.s. (This 0-1 law applies to any L\\'evy process.) Then we show that if the function $f$ is H\\\"older$(1/2)$, then $B+f$ is intersection equivalent to $B$. Moreover, $B+f$ has double points a.s. in dimensions $d\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2987","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"}