Proceedings of the Centre for Mathematics and its Applications

Wrapping Brownian motion and heat kernels on compact Lie groups

David Maher

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Abstract

The fundamental solution of the heat equation on $\mathboldR^n$ is known as the heat kernel which is also the transition density of a Brownian motion. Similar statements hold when $\mathboldR^n$ is replaced by a Lie group. We briefly demonstrate how the results on $\mathboldR^n$ concerning the heat kernel and Brownian motion may be easily transferred to compact Lie groups using the wrapping map of Dooley and Wildberger.

Article information

Source
CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis and Related Topics". Alan McIntosh and Pierre Portal, eds. Proceedings of the Centre for Mathematics and its Applications, v. 42. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2007), 91-99

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416321170

Mathematical Reviews number (MathSciNet)
MR2328514

Zentralblatt MATH identifier
1183.22004

Citation

Maher, David. Wrapping Brownian motion and heat kernels on compact Lie groups. CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis and Related Topics", 91--99, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2007. https://projecteuclid.org/euclid.pcma/1416321170


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