{"paper":{"title":"Minimax of an n-dimensional Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Konstantin Tikhomirov, Pierre Youssef","submitted_at":"2015-04-07T23:19:54Z","abstract_excerpt":"For some absolute constants $c$, $n_0$ and any $n\\geq n_0$, we show that with probability close to one the convex hull of the $n$-dimensional Brownian motion ${\\rm conv}\\{BM_n(t):\\, t\\in[1,2^{cn}]\\}$ does not contain the origin. The result can be interpreted as an estimate of the minimax of the Gaussian process $\\{ \\langle \\bar{u},BM_n(t)\\rangle,\\, \\bar{u}\\in S^{n-1},\\, t\\in [1,2^{cn}]\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01778","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"}