78789 20201130083155.0 sideral 111119 ART-2017-111119 eng Alonso-Gutiérrez, David Distribution of mass in high-dimensional convex bodies 2017 Access copy available to the general public Unrestricted In 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. info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion 72 (2017), 7-32 Rev. Acad. Cienc. Exactas, Fís.-Quím. Nat. Zaragoza Revista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza 0370-3207 http://www.raczar.es/webracz/ImageServlet?mod=publicaciones&subMod=revistas&car=revista72&archivo=007DavidAlonso.pdf Texto completo de la revista 468599 http://zaguan.unizar.es/record/78789/files/texto_completo.pdf Postprint 54859 http://zaguan.unizar.es/record/78789/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:78789 articulos driver 2020-11-30-07:57:32 ARTICLE