On Gilles Pisier's approach to gaussian concentration, isoperimetry and Poincaré-type inequalities

Abstract

We discuss a natural extension of Gilles Pisier's approach to the study of measure concentration, isoperimetry and Poincaré-type inequalities. This approach allows one to explore counterparts of various results about Gaussian measure in the class of rotationally invariant probability distribution on Euclidean spaces, including multidimensional Cauchy measures.