Brownian Motion and the Heat Kernels of Iwasawa $NA$-Type Groups

Abstract: Let $G$ be a semisimple Lie group with a finite centre and Iwasawa decomposition $NAK$. We shall consider the heat equation on $NA$ and prove a structure theorem for a diffusion on the group which is typically called a Brownian motion. This theorem then shows how we may calculate the heat kernel of real hyperbolic space in a relatively easy fashion.

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