Journal of Lie Theory

no. 2
Brownian Motion and the Heat Kernels of Iwasawa NA-Type Groups
Journal of Lie Theory, Volume 11 (2001) no. 2, pp. 469-481
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.
DOI: 10.5802/jolt.243
Classification: 22E30
Keywords: semisimple Lie group, Iwasawa decomposition, heat equation, stochastic differential equation, heat kernel 
@article{JOLT_2001_11_2_a10,
     author = {M. J. Cornwall},
     title = {Brownian {Motion} and the {Heat} {Kernels} of {Iwasawa} {NA-Type} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {469--481},
     year = {2001},
     volume = {11},
     number = {2},
     doi = {10.5802/jolt.243},
     zbl = {0982.22009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.243/}
}
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M. J. Cornwall. Brownian Motion and the Heat Kernels of Iwasawa NA-Type Groups. Journal of Lie Theory, Volume 11 (2001) no. 2, pp. 469-481. doi: 10.5802/jolt.243

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