{"paper":{"title":"Spectral gaps, symmetries and log-concave perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Bo'az Klartag, Franck Barthe","submitted_at":"2019-07-03T09:56:13Z","abstract_excerpt":"We discuss situations where perturbing a probability measure on $\\mathbb{R}^n$ does not deteriorate its Poincar\\'e constant by much. A particular example is the symmetric exponential measure in $\\mathbb{R}^n$, even log-concave perturbations of which have Poincar\\'e constants that grow at most logarithmically with the dimension. This leads to estimates for the Poincar\\'e constants of $(n/2)$-dimensional sections of the unit ball of $\\ell_p^n$ for $1 \\leq p \\leq 2$, which are optimal up to logarithmic factors. We also consider symmetry properties of the eigenspace of the Laplace-type operator as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01823","kind":"arxiv","version":2},"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"}