Speaker: Nathaniel Eldredge, School of Mathematical Sciences, University of Northern Colorado
ABSTRACT
A classic example of a hypoelliptic diffusion is a two-dimensional Brownian motion coupled with its Levy area process; it can be viewed as a Brownian motion on the three-dimensional Heisenberg group. Despite being driven by a Brownian motion with "too few" dimensions, this process is still able to diffuse smoothly through all of R^3; its law has a smooth density (or heat kernel) with respect to Lebesgue measure. In this talk, I will discuss an extension of this classical result to Heisenberg-like groups of infinite dimension, modeled on abstract Wiener spaces. Our approach is based on an interesting stochastic formula for the heat kernel, and a key question is how to interpret "smoothness of density" in a setting where there is no obvious reference measure. This is joint work with Bruce Driver and Tai Melcher.