{"paper":{"title":"Packing-Dimension Profiles and Fractional Brownian Motion","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Davar Khoshnevisan, Yimin Xiao","submitted_at":"2007-05-01T16:30:48Z","abstract_excerpt":"In order to compute the packing dimension of orthogonal projections\n  Falconer and Howroyd (1997) introduced a family of packing dimension profiles ${\\rm Dim}_s$ that are parametrized by real numbers $s>0$. Subsequently, Howroyd (2001) introduced alternate $s$-dimensional packing dimension profiles $\\hbox{${\\rm P}$-$\\dim$}_s$ and proved, among many other things, that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all integers $s>0$ and all analytic sets $E\\subseteq\\R^N$. The goal of this article is to prove that $\\hbox{${\\rm P}$-$\\dim$}_s E={\\rm Dim}_s E$ for all real numbers $s>0$ and analyt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.0135","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"}