{"paper":{"title":"Generalized Dual Sudakov Minoration via Dimension Reduction - A Program","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Emanuel Milman, Grigoris Paouris, Shahar Mendelson","submitted_at":"2016-10-28T15:58:06Z","abstract_excerpt":"We propose a program for establishing a conjectural extension to the class of (origin-symmetric) log-concave probability measures $\\mu$, of the classical dual Sudakov Minoration on the expectation of the supremum of a Gaussian process: \\begin{equation} \\label{eq:abstract} M(Z_p(\\mu), C \\int ||x||_K d\\mu \\cdot K) \\leq \\exp(C p) \\;\\;\\, \\forall p \\geq 1 . \\end{equation} Here $K$ is an origin-symmetric convex body, $Z_p(\\mu)$ is the $L_p$-centroid body associated to $\\mu$, $M(A,B)$ is the packing-number of $B$ in $A$, and $C > 0$ is a universal constant. The Program consists of first establishing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09287","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"}