000078789 001__ 78789 000078789 005__ 20201130083155.0 000078789 0248_ $$2sideral$$a111119 000078789 037__ $$aART-2017-111119 000078789 041__ $$aeng 000078789 100__ $$aAlonso-Gutiérrez, David 000078789 245__ $$aDistribution of mass in high-dimensional convex bodies 000078789 260__ $$c2017 000078789 5060_ $$aAccess copy available to the general public$$fUnrestricted 000078789 5203_ $$aIn this paper we will explore the interaction between convex geometry and proba-bility in the study of the distribution of volume in high-dimensional convex bodies. On the one hand, a convex body K in Rn can be understood as a probability space whenthe normalized Lebesgue measure is considered. Thus, probabilistic tools become veryhandy in the study of the behavior of a random vector uniformly distributed inK.This leads to the understanding of how the volume is distributed in a convex body andthe obtention of geometric inequalities. On the other hand, when considering lower-dimensional marginals of the uniform probability measure onK, we leave the class ofuniform probabilities on convex bodies but remain in the class of log-concave probabilities. Many geometric inequalities can be extended to the context of log-concaveprobabilities, leading to functional inequalities for log- concave functions. 000078789 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P 000078789 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000078789 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000078789 773__ $$g72 (2017), 7-32$$pRev. Acad. Cienc. Exactas, Fís.-Quím. Nat. Zaragoza$$tRevista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza$$x0370-3207 000078789 85641 $$uhttp://www.raczar.es/webracz/ImageServlet?mod=publicaciones&subMod=revistas&car=revista72&archivo=007DavidAlonso.pdf$$zTexto completo de la revista 000078789 8564_ $$s468599$$uhttps://zaguan.unizar.es/record/78789/files/texto_completo.pdf$$yPostprint 000078789 8564_ $$s54859$$uhttps://zaguan.unizar.es/record/78789/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000078789 909CO $$ooai:zaguan.unizar.es:78789$$particulos$$pdriver 000078789 951__ $$a2020-11-30-07:57:32 000078789 980__ $$aARTICLE