{"paper":{"title":"Moments of the maximal number of empty simplices of a random point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Daniel Temesvari","submitted_at":"2016-12-22T08:10:21Z","abstract_excerpt":"For a finite set $X$ of $n$ points from $\\mathbb{R}^M$, the degree of an $M$-element subset $\\{x_1,\\dots,x_M\\}$ of $X$ is defined as the number of $M$-simplices that can be constructed from this $M$-element subset using an additional point $z\\in X$, such that no further point of $X$ lies in the interior of this $M$-simplex. Furthermore, the degree of $X$, denoted by $\\textrm{deg} (X)$, is the maximal degree of any of its $M$-element subsets.\n  The purpose of this paper is to show that the moments of the degree of $X$ satisfy $\\mathbb{E}\\left[\\textrm{deg} (X)^k\\right] \\geq c n^k / \\log n$, for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07481","kind":"arxiv","version":2},"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"}