Title: Randomized isoperimetric inequalities
Speaker: Peter Pivovarov (Assistant Professor, University of Missouri)
Abstract: The focus of my talk will be stochastic forms of isoperimetric inequalities for convex sets. In particular, I will discuss the Brunn-Minkowski inequality and some of its recent extensions. I will show how one can view these as global inequalities that arise through random approximation procedures in which stochastic dominance holds at each stage. By laws of large numbers, these randomized versions recover the global (non-random) inequalities. I will discuss when such stochastic dominance arises, the use of rearrangement inequalities and applications to small deviation probabilities.