{"paper":{"title":"A universal result for consecutive random subdivision of polygons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nguyen Tuan Minh, Stanislav Volkov","submitted_at":"2015-06-16T12:34:28Z","abstract_excerpt":"We consider consecutive random subdivision of polygons described as follows. Given an initial convex polygon with $d\\ge 3$ edges, we choose a point at random on each edge, such that the proportions in which these points divide edges are i.i.d. copies of some random variable $\\xi$. These new points form a new (smaller) polygon. By repeatedly implementing this procedure we obtain a sequence of random polygons. The aim of this paper is to show that under very mild non-degenerateness conditions on $\\xi$, the shapes of these polygons eventually become \"flat\" The convergence rate to flatness is also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04942","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"}