162959 20251017144643.0 doi 10.1016/j.jco.2025.101993 sideral 145433 ART-2026-145433 eng Alonso-Gutiérrez, David Universidad de Zaragoza (orcid)0000-0003-1256-3671 Borell's inequality and mean width of random polytopes via discrete inequalities 2026 Access copy available to the general public Unrestricted Borell's inequality states the existence of a positive absolute constant C>0 such that for every 1≤p≤q(E|〈X,en〉|p)1p≤(E|〈X,en〉|q)1q≤Cqp(E|〈X,en〉|p)1p, whenever X is a random vector uniformly distributed on any convex body K⊆Rn and (ei)i=1n is the standard canonical basis in Rn. In this paper, we will prove a discrete version of this inequality, which will hold whenever X is a random vector uniformly distributed on K∩Zn for any convex body K⊆Rn containing the origin in its interior. We will also make use of such discrete version to obtain discrete inequalities from which we can recover the estimate Ew(KN)∼w(Zlog⁡N(K)) for any convex body K containing the origin in its interior, where KN is the centrally symmetric random polytope KN=conv{±X1,…,±XN} generated by independent random vectors uniformly distributed on K, Zp(K) is the Lp-centroid body of K for any p≥1, and w(⋅) denotes the mean width. info:eu-repo/grantAgreement/ES/DGA/E48-23R info:eu-repo/grantAgreement/ES/MICIU/PID2021-122126NB-C32 info:eu-repo/grantAgreement/ES/MICIU/PID2022-137294NB-I00 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion García-Lirola, Luis C. Universidad de Zaragoza (orcid)0000-0001-9211-4475 2006 015 Universidad de Zaragoza Dpto. Matemáticas Área Análisis Matemático 92 (2026), 101993 [25 pp.] J. complex. JOURNAL OF COMPLEXITY 0885-064X 937781 http://zaguan.unizar.es/record/162959/files/texto_completo.pdf Versión publicada 1409972 http://zaguan.unizar.es/record/162959/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:162959 articulos driver 2025-10-17-14:33:06 ARTICLE