{"paper":{"title":"Uniform dimension results for fractional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Rich\\'ard Balka, Yuval Peres","submitted_at":"2015-09-10T01:10:17Z","abstract_excerpt":"Kaufman's dimension doubling theorem states that for a planar Brownian motion $\\{\\mathbf{B}(t): t\\in [0,1]\\}$ we have $$\\mathbb{P}(\\dim \\mathbf{B}(A)=2\\dim A \\textrm{ for all } A\\subset [0,1])=1,$$ where $\\dim$ may denote both Hausdorff dimension $\\dim_H$ and packing dimension $\\dim_P$. The main goal of the paper is to prove similar uniform dimension results in the one-dimensional case. Let $0<\\alpha<1$ and let $\\{B(t): t\\in [0,1]\\}$ be a fractional Brownian motion of Hurst index $\\alpha$. For a deterministic set $D\\subset [0,1]$ consider the following statements: $$(A) \\quad \\mathbb{P}(\\dim_H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02979","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"}