Wrapping Brownian motion and heat kernels on compact Lie groups

Abstract

The fundamental solution of the heat equation on $\mathboldR^n$ is known as the heat kernel which is also the transition density of a Brownian motion. Similar statements hold when $\mathboldR^n$ is replaced by a Lie group. We briefly demonstrate how the results on $\mathboldR^n$ concerning the heat kernel and Brownian motion may be easily transferred to compact Lie groups using the wrapping map of Dooley and Wildberger.