{"paper":{"title":"Random parking, Euclidean functionals, and rubber elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Antoine Gloria, Mathew D. Penrose","submitted_at":"2012-03-06T09:00:54Z","abstract_excerpt":"We study subadditive functions of the random parking model previously analyzed by the second author. In particular, we consider local functions $S$ of subsets of $\\mathbb{R}^d$ and of point sets that are (almost) subadditive in their first variable. Denoting by $\\xi$ the random parking measure in $\\mathbb{R}^d$, and by $\\xi^R$ the random parking measure in the cube $Q_R=(-R,R)^d$, we show, under some natural assumptions on $S$, that there exists a constant $\\bar{S}\\in \\mathbb{R}$ such that % $$ \\lim_{R\\to +\\infty} \\frac{S(Q_R,\\xi)}{|Q_R|}\\,=\\,\\lim_{R\\to +\\infty}\\frac{S(Q_R,\\xi^R)}{|Q_R|}\\,=\\,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1140","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"}