{"paper":{"title":"Ornstein-Uhlenbeck pinball: I. Poincar\\'e inequalities in a punctured domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnaud Guillin, Emmanuel Boissard (IMT), Laurent Miclo (IMT), Patrick Cattiaux (IMT)","submitted_at":"2013-09-04T11:42:30Z","abstract_excerpt":"In this paper we study the Poincar\\'e constant for the Gaussian measure restricted to $D=\\R^d - B(y,r)$ where $B(y,r)$ denotes the Euclidean ball with center $y$ and radius $r$, and $d\\geq 2$. We also study the case of the $l^\\infty$ ball (the hypercube). This is the first step in the study of the asymptotic behavior of a $d$-dimensional Ornstein-Uhlenbeck process in the presence of obstacles with elastic normal reflections (the Ornstein-Uhlenbeck pinball) we shall study in a companion paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0986","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"}