{"paper":{"title":"Probabilistic discrepancy bound for Monte Carlo point sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Christoph Aistleitner, Markus Hofer","submitted_at":"2012-11-05T22:25:04Z","abstract_excerpt":"By a profound result of Heinrich, Novak, Wasilkowski, and Wo{\\'z}niakowski the inverse of the star-discrepancy $n^*(s,\\ve)$ satisfies the upper bound $n^*(s,\\ve) \\leq c_{\\mathrm{abs}} s \\ve^{-2}$. This is equivalent to the fact that for any $N$ and $s$ there exists a set of $N$ points in $[0,1]^s$ whose star-discrepancy is bounded by $c_{\\mathrm{abs}} s^{1/2} N^{-1/2}$. The proof is based on the observation that a random point set satisfies the desired discrepancy bound with positive probability. In the present paper we prove an applied version of this result, making it applicable for computat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1058","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"}