{"paper":{"title":"A general study of extremes of stationary tessellations with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nicolas Chenavier","submitted_at":"2013-10-21T19:00:43Z","abstract_excerpt":"Let $\\mathfrak{m}$ be a random tessellation in $\\mathbf{R}^d$ observed in a bounded Borel subset $W$ and $f(\\cdot)$ be a measurable function defined on the set of convex bodies. To each cell $C$ of $\\mathfrak{m}$ we associate a point $z(C)$ which is the nucleus of $C$. Applying $f(\\cdot)$ to all the cells of $\\mathfrak{m}$, we investigate the order statistics of $f(C)$ over all cells $C\\in\\mathfrak{m}$ with nucleus in $\\mathbf{W}_{\\rho}=\\rho^{1/d}W$ when $\\rho$ goes to infinity. Under a strong mixing property and a local condition on $\\mathfrak{m}$ and $f(\\cdot)$, we show a general theorem whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5675","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"}