{"paper":{"title":"Logarithmic Sobolev inequalities in discrete product spaces: a proof by a transportation cost distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Katalin Marton","submitted_at":"2015-07-10T08:20:49Z","abstract_excerpt":"The aim of this paper is to prove an inequality between relative entropy and the sum of average conditional relative entropies of the following form: For a fixed probability measure $q^n$ on $\\mathcal X^n$, ($\\mathcal X$ is a finite set), and any probability measure $p^n=\\mathcal L(Y^n)$ on $\\mathcal X^n$, we have \\begin{equation}\\label{*} D(p^n||q^n)\\leq Const. \\sum_{i=1}^n \\Bbb E_{p^n} D(p_i(\\cdot|Y_1,\\dots, Y_{i-1},Y_{i+1},\\dots, Y_n) || q_i(\\cdot|Y_1,\\dots, Y_{i-1},Y_{i+1},\\dots, Y_n)), \\end{equation} where $p_i(\\cdot|y_1,\\dots, y_{i-1},y_{i+1},\\dots, y_n)$ and $q_i(\\cdot|x_1,\\dots, x_{i-1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02803","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"}