{"paper":{"title":"Spectral gap for spherically symmetric log-concave probability measures, and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ald\\'eric Joulin (IMT), Michel Bonnefont (IMB), Yutao ma","submitted_at":"2014-06-18T07:07:12Z","abstract_excerpt":"Let $\\mu$ be a probability measure on $\\rr^n$ ($n \\geq 2$) with Lebesgue density proportional to $e^{-V (\\Vert x\\Vert )}$, where $V : \\rr_+ \\to \\rr$ is a smooth convex potential. We show that the associated spectral gap in $L^2 (\\mu)$ lies between $(n-1) / \\int_{\\rr^n} \\Vert x\\Vert ^2 \\mu(dx)$ and $n / \\int_{\\rr^n} \\Vert x\\Vert ^2 \\mu(dx)$, improving a well-known two-sided estimate due to Bobkov. Our Markovian approach is remarkably simple and is sufficiently robust to be extended beyond the log-concave case, at the price of potentially modifying the underlying dynamics in the energy, leading "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4621","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"}