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Large deviation bounds for matrix Brownian motion

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Inventiones mathematicae Aims and scope

Abstract.

We prove large deviation bounds for the convergence of Hermitian matrix valued Brownian motion towards free Brownian motion. As a consequence, we obtain upper and lower bounds on the microstates entropy introduced by Voiculescu [24].

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Authors and Affiliations

  1. CNRS, Département de Mathématiques et Applications, École Normale Supérieure, 45, rue d’Ulm, 75005 Paris, France (e-mail: Philippe.Biane@ens.fr), , , , , , FR

    P. Biane

  2. LSP, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France (e-mail: capitain@cict.fr), , , , , , FR

    M. Capitaine

  3. UMPA, Ecole Normale Supérieure de Lyon, 46 allée d’Italie, 69007 Lyon, France (e-mail: Alice.Guionnet@umpa.ens-lyon.fr), , , , , , FR

    A. Guionnet

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  1. P. Biane
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  2. M. Capitaine
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  3. A. Guionnet
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Oblatum 5-VIII-2002 & 18-XI-2002¶Published online: 24 February 2003

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Biane, P., Capitaine, M. & Guionnet, A. Large deviation bounds for matrix Brownian motion. Invent. math. 152, 433–459 (2003). https://doi.org/10.1007/s00222-002-0281-4

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  • DOI: https://doi.org/10.1007/s00222-002-0281-4

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