{"paper":{"title":"Limit shape of random convex polygonal lines: Even more universality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Leonid V. Bogachev","submitted_at":"2011-11-15T13:47:34Z","abstract_excerpt":"The paper concerns the limit shape (under some probability measure) of convex polygonal lines with vertices on $\\mathbb{Z}_+^2$, starting at the origin and with the right endpoint $n=(n_1,n_2)\\to\\infty$. In the case of the uniform measure, an explicit limit shape $\\gamma^*:=\\{(x_1,x_2)\\in\\mathbb{R}_+^2\\colon \\sqrt{1-x_1}+\\sqrt{x_2}=1\\}$ was found independently by Vershik (1994), B\\'ar\\'any (1995), and Sinai (1994). Recently, Bogachev and Zarbaliev (2011) proved that the limit shape $\\gamma^*$ is universal for a certain parametric family of multiplicative probability measures generalizing the u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3529","kind":"arxiv","version":3},"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"}