Geodesic
Wrapping Brownian Motion and Heat Kernels. I: Compact Lie Groups
Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1149-1168

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An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and Wildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel.
Classification : 43A77, 22E30, 58J65
Mots-clés : Compact Lie group, Brownian motion, wrapping map 
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     author = {D. G. Maher },
     title = {Wrapping {Brownian} {Motion} and {Heat} {Kernels.} {I:} {Compact} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {1149--1168},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a11/}
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D. G. Maher . Wrapping Brownian Motion and Heat Kernels. I: Compact Lie Groups. Journal of Lie theory, Tome 22 (2012) no. 4, pp. 1149-1168. http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a11/