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Matrix valued Brownian motion and a paper by Polya

Abstract : This paper has two parts which are largely independent. In the first one I recall some known facts on matrix valued Brownian motion, which are not so easily found in this form in the literature. I will study three types of matrices, namely Hermitian matrices, complex invertible matrices, and unitary matrices, and try to give a precise description of the motion of eigenvalues (or singular values) in each case.
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Contributor : Philippe Biane <>
Submitted on : Monday, September 12, 2011 - 4:32:58 PM
Last modification on : Wednesday, February 26, 2020 - 7:06:05 PM

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Philippe Biane. Matrix valued Brownian motion and a paper by Polya. Catherine Donati-Martin, Michel Émery, Alain Rouault, Christophe Stricker. Séminaire de Probabilités XLII, 1979 (1), Springer, pp.171-185, 2009, Lecture Notes in Mathematics, ⟨10.1007/978-3-642-01763-6_7⟩. ⟨hal-00622781⟩



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