Stochastics Seminar

Speaker: Dr. Ming Liao

Title: Convolution of probability measures on compact Lie groups

Abstract:  The convolution power of a probability measure on a compact group G is expected to converge to the normalized Haar measure.  The weak convergence is guaranteed by the classical Ito-Kawasa Theorem, and there are also some more recent results on convergence in total variation norm using Fourier analytic method (Peter-Weyl Theorem).  We may also consider the convergence of a convolution semigroup of probability measures on G.  When G is a Lie group, Hunt's generator formula provides a convenient tool to study convolution semigroups.