{"paper":{"title":"Robust dimension free isoperimetry in Gaussian space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elchanan Mossel, Joe Neeman","submitted_at":"2012-02-19T02:28:48Z","abstract_excerpt":"We prove the first robust dimension free isoperimetric result for the standard Gaussian measure $\\gamma_n$ and the corresponding boundary measure $\\gamma_n^+$ in $\\mathbb {R}^n$. The main result in the theory of Gaussian isoperimetry (proven in the 1970s by Sudakov and Tsirelson, and independently by Borell) states that if $\\gamma_n(A)=1/2$ then the surface area of $A$ is bounded by the surface area of a half-space with the same measure, $\\gamma_n^+(A)\\leq(2\\pi)^{-1/2}$. Our results imply in particular that if $A\\subset \\mathbb {R}^n$ satisfies $\\gamma_n(A)=1/2$ and $\\gamma_n^+(A)\\leq(2\\pi)^{-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4124","kind":"arxiv","version":3},"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"}