engAlonso-Gutiérrez, DavidDistribution of mass in high-dimensional convex bodiesART-2017-111119In 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.2017http://zaguan.unizar.es/record/78789http://zaguan.unizar.es/record/78789oai:zaguan.unizar.es:78789info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-PRevista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza 72 (2017), 7-32by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess