Geodesic
Brownian Motion and the Heat Kernels of Iwasawa NA-Type Groups
Journal of Lie theory, Tome 11 (2001) no. 2, pp. 469-481 Cet article a éte moissonné depuis la source Heldermann Verlag

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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. 
@article{JLT_2001_11_2_JLT_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},
     url = {http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a10/}
}
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M. J. Cornwall . Brownian Motion and the Heat Kernels of Iwasawa NA-Type Groups. Journal of Lie theory, Tome 11 (2001) no. 2, pp. 469-481. http://geodesic.mathdoc.fr/item/JLT_2001_11_2_JLT_2001_11_2_a10/