{"paper":{"title":"Concentration inequalities for non-Lipschitz functions with bounded derivatives of higher order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.FA"],"primary_cat":"math.PR","authors_text":"Pawe{\\l} Wolff, Rados{\\l}aw Adamczak","submitted_at":"2013-04-05T21:41:40Z","abstract_excerpt":"Building on the inequalities for homogeneous tetrahedral polynomials in independent Gaussian variables due to R. Lata{\\l}a we provide a concentration inequality for non-necessarily Lipschitz functions $f\\colon \\R^n \\to \\R$ with bounded derivatives of higher orders, which hold when the underlying measure satisfies a family of Sobolev type inequalities $\\|g- \\E g\\|_p \\le C(p)\\|\\nabla g\\|_p.$\n  Such Sobolev type inequalities hold, e.g., if the underlying measure satisfies the log-Sobolev inequality (in which case $C(p) \\le C\\sqrt{p}$) or the Poincar\\'e inequality (then $C(p) \\le Cp$). Our concent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1826","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"}