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Cyril Roberto, U. Paris-Est Print
Friday, 08 May 2009, 14:30 - 15:30

Isoperimetry for product probability measures

Cyril Roberto, Université de Paris-Est, Marne la Vallée

Abstract: We shall give a short overview on the isoperimetric problem for product probability measures. An isoperimetric inequality is a lower bound on the boundary measure of sets in terms of their measure. Finding the optimal sets (of given measure and of minimal boundary measure) is very difficult, and the only hope is to estimate the isoperimetric function. This is well understood on the line (Bobkov) and for the product of standard Gaussian measures (Sudakov-Tsirel'son, Borell). We shall start by recalling those known results. Then, we shall explain how functional inequalities can be used to get dimension free isoperimetric inequalities for measures between exponential and Gaussian. Also, using the transport of mass technique we shall derviveisoperimetric inequalities (depending on the dimension) for measures with tails larger than exponential.

Location: Campus Plaine
Contact: Jacqueline Bottemanne, This e-mail address is being protected from spam bots, you need JavaScript enabled to view it