{"paper":{"title":"Universal Scaling Limits for Generalized Gamma Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Julian Grote","submitted_at":"2018-08-29T13:06:42Z","abstract_excerpt":"Fix a space dimension $d\\ge 2$, parameters $\\alpha > -1$ and $\\beta \\ge 1$, and let $\\gamma_{d,\\alpha, \\beta}$ be the probability measure of an isotropic random vector in $\\mathbb{R}^d$ with density proportional to \\begin{align*} ||x||^\\alpha\\, \\exp\\left(-\\frac{\\|x\\|^\\beta}{\\beta}\\right), \\qquad x\\in \\mathbb{R}^d. \\end{align*} By $K_\\lambda$, we denote the Generalized Gamma Polytope arising as the random convex hull of a Poisson point process in $\\mathbb{R}^d$ with intensity measure $\\lambda\\gamma_{d,\\alpha,\\beta}$, $\\lambda>0$. We establish that the scaling limit of the boundary of $K_\\lambda"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09779","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"}