Laplacian and Brownian motion on positive definite matrices, revisited

We present explicit expression for the Laplace–Beltrami operator on the symmetric space of positive definite matrices by using the Iwasawa decomposition and study the corresponding diffusion process, the Brownian motion. We show that some inductive arguments in the dimensions work.

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Bibliographic Details
Published in:	Statistics & probability letters Vol. 193; p. 109696
Main Authors:	Matsumoto, Hiroyuki, Otani, Jun
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-02-2023
Subjects:	Brownian motion Diffusion process Laplace–Beltrami operator Positive definite matrices Symmetric space secondary Brownian motion Laplace–Beltrami operator Symmetric space Diffusion process Positive definite matrices primary
Online Access:	Get full text
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Description
Summary:	We present explicit expression for the Laplace–Beltrami operator on the symmetric space of positive definite matrices by using the Iwasawa decomposition and study the corresponding diffusion process, the Brownian motion. We show that some inductive arguments in the dimensions work.
ISSN:	0167-7152 1879-2103
DOI:	10.1016/j.spl.2022.109696