{"paper":{"title":"Moment measures and stability for Gaussian inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander V. Kolesnikov, Egor D. Kosov","submitted_at":"2017-12-30T15:08:45Z","abstract_excerpt":"Let $\\gamma$ be the standard Gaussian measure on $\\mathbb{R}^n$ and let $\\mathcal{P}_{\\gamma}$ be the space of probability measures that are absolutely continuous with respect to $\\gamma$. We study lower bounds for the functional $\\mathcal{F}_{\\gamma}(\\mu) = {\\rm Ent}(\\mu) - \\frac{1}{2} W^2_2(\\mu, \\nu)$, where $\\mu \\in \\mathcal{P}_{\\gamma}, \\nu \\in \\mathcal{P}_{\\gamma}$, ${\\rm Ent}(\\mu) = \\int \\log\\bigl( \\frac{\\mu}{\\gamma}\\bigr) d \\mu$ is the relative Gaussian entropy, and $W_2$ is the quadratic Kantorovich distance. The minimizers of $\\mathcal{F}_{\\gamma}$ are solutions to a dimension-free Ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00140","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"}