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Journal of Lie Theory, Vol. 11, No. 2, pp. 469-481 (2001)
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#
Brownian Motion and the Heat Kernels of Iwasawa $NA$-Type Groups

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M. J. Cornwall

1 Martin Place

Sydney N.S.W. 2000

Australia

JCornwal@macquarie.com.au

**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.

**Full text of the article:**

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