{"paper":{"title":"Concentration inequalities via zero bias couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Larry Goldstein, Umit Islak","submitted_at":"2013-04-18T01:25:43Z","abstract_excerpt":"The tails of the distribution of a mean zero, variance $\\sigma^2$ random variable $Y$ satisfy concentration of measure inequalities of the form $\\mathbb{P}(Y \\ge t) \\le \\exp(-B(t))$ for $$ B(t)=\\frac{t^2}{2( \\sigma^2 + ct)} \\quad \\mbox{for $t \\ge 0$, and} \\quad B(t)=\\frac{t}{c}\\left( \\log t - \\log \\log t - \\frac{\\sigma^2}{c}\\right) \\quad \\mbox{for $t>e$} $$ whenever there exists a zero biased coupling of $Y$ bounded by $c$, under suitable conditions on the existence of the moment generating function of $Y$. These inequalities apply in cases where $Y$ is not a function of independent variables,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5001","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"}