{"paper":{"title":"Moment comparisons, Sudakov inequalities and entropy of centroid bodies","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"Antonios Hmadi, Dimitris-Marios Liakopoulos","submitted_at":"2026-08-11T12:25:33Z","abstract_excerpt":"Let $X$ be an isotropic log-concave random vector in $\\mathbb{R}^n$ and let $G$ be standard Gaussian. Starting from the first moment comparison for gauges, we derive corresponding estimates at arbitrary moment orders. For every gauge $\\phi$ and every $q\\geqslant 1$, $$ \\|\\phi(G)\\|_q\\leqslant C\\sqrt{\\ln(en)+q}\\,\\|\\phi(X)\\|_q,\\qquad \\|\\phi(X)\\|_q\\leqslant C\\left(\\sqrt{\\ln(en)}+\\psi(X)\\sqrt q\\right)\\|\\phi(G)\\|_q. $$ Applied to support functions, this gives the sharp worst case order $C\\sqrt{\\ln(en)}$ for the $L_2$-Sudakov constant and quantitative $L_p$-Sudakov estimates. Combining, at each level"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10853","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.10853/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}