{"paper":{"title":"On sharp bounds for marginal densities of product measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Galyna Livshyts, Grigoris Paouris, Peter Pivovarov","submitted_at":"2015-07-28T20:36:13Z","abstract_excerpt":"We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if $f$ is a probability density on $\\R^n$ of the form $f(x)=\\prod_{i=1}^n f_i(x_i)$, where each $f_i$ is a density on $\\R$, say bounded by one, then the density of any marginal $\\pi_E(f)$ is bounded by $2^{k/2}$, where $k$ is the dimension of $E$. The proof relies on an adaptation of Ball's approach to cube slicing, carried out for functions. Motivated by inequalities for dual affine quermassintegrals, we also prove an isoperimetric inequality for certain averages of the marginals of s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07949","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"}