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Matrix Valued Brownian Motion and a Paper by Pólya

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Séminaire de Probabilités XLII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1979))

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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Author information

Authors and Affiliations

  1. CNRS, Laboratoire d’Informatique Institut Gaspard Monge, Université Paris-Est 5 bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée, cedex 2, France

    Philippe Biane

Authors
  1. Philippe Biane
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Correspondence to Philippe Biane .

Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. Inst. Recherche, Mathématiques Avancées, Université Strasbourg I, rue René Descartes 7, Strasbourg CX, 67084, France

    Michel Émery

  3. Laboratoire de Mathematiques, Université de Versailles, av. des Etats-Unis 45, Versailles CX, 78035, France

    Alain Rouault

  4. CNRS UMR 6623, Lab. de Mathématiques, Université Besancon, route de Gray 16, Besancon CX, 25030, France

    Christophe Stricker

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Biane, P. (2009). Matrix Valued Brownian Motion and a Paper by Pólya. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLII. Lecture Notes in Mathematics(), vol 1979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01763-6_7

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