{"paper":{"title":"Universality of the limit shape of convex lattice polygonal lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Leonid V. Bogachev, Sakhavat M. Zarbaliev","submitted_at":"2008-07-23T16:00:06Z","abstract_excerpt":"Let ${\\varPi}_n$ be the set of convex polygonal lines $\\varGamma$ with vertices on $\\mathbb {Z}_+^2$ and fixed endpoints $0=(0,0)$ and $n=(n_1,n_2)$. We are concerned with the limit shape, as $n\\to\\infty$, of \"typical\" $\\varGamma\\in {\\varPi}_n$ with respect to a parametric family of probability measures $\\{P_n^r,0<r<\\infty\\}$ on ${\\varPi}_n$, including the uniform distribution ($r=1$) for which the limit shape was found in the early 1990s independently by A. M. Vershik, I. B\\'ar\\'any and Ya. G. Sinai. We show that, in fact, the limit shape is universal in the class $\\{P^r_n\\}$, even though $P^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.3682","kind":"arxiv","version":4},"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"}