EVENT DETAILS AND ABSTRACT

Title: Log-Sobolev inequalities on the horizontal path space of a totally geodesic foliation
Speaker: Qi Feng
Speaker Info: Purdue University
Brief Description:
Special Note:
Abstract:

We develop a Malliavin calculus on the horizontal path space of a totally geodesic Riemannian foliation. As a first application, under suitable assumptions, we prove a log-Sobolev inequality for a natural one-parameter family of infinite-dimensional Ornstein-Uhlenbeck type operators. As a second application, we obtain concentration and tail estimates for the horizontal Brownian motion of the foliation. Our result uses the Bochner-Weitzenb\"ock formula on totally geodesic foliations earlier proved by Baudoin-Kim-Wang.