{"paper":{"title":"An explicit bound on the Logarithmic Sobolev constant of weakly dependent random variables","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Katalin Marton","submitted_at":"2006-05-15T15:40:50Z","abstract_excerpt":"We prove logarithmic Sobolev inequality for measures $$ q^n(x^n)=\\text{dist}(X^n)=\\exp\\bigl(-V(x^n)\\bigr), \\quad x^n\\in \\Bbb R^n, $$ under the assumptions that: (i) the conditional distributions $$ Q_i(\\cdot| x_j, j\\neq i)=\\text{dist}(X_i| X_j= x_j, j\\neq i) $$ satisfy a logarithmic Sobolev inequality with a common constant $\\rho$, and  (ii) they also satisfy some condition expressing that the mixed partial derivatives of the Hamiltonian $V$ are not too large relative to $\\rho$. \\bigskip Condition (ii) has the form that the norms of some matrices defined in terms of the mixed partial derivativ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605397","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"}