Distribution of mass in high-dimensional convex bodies

Alonso-Gutiérrez, David

Resumen: 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.

Idioma: Inglés

Año: 2017

Publicado en: Revista de la Academia de Ciencias Exactas, Físico-Químicas y Naturales de Zaragoza 72 (2017), 7-32
ISSN: 0370-3207

Originalmente disponible en: Texto completo de la revista

Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-P

Tipo y forma: Artículo (PostPrint)