Concentration phenomena in high dimensional geometry

Abstract

The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The topic has a broad audience going from algorithmic convex geometry to random matrices. We have tried to emphasize different problems relating these areas of research. Another connected area is the study of probability in Banach spaces where some concentration phenomena are related with good comparisons between the weak and the strong moments of a random vector.

arXiv commentThis paper is written after a plenary talk given in August 2012 at the "Journées MAS" organized in Clermont Ferrand. To appear in ESAIM Proceedings