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July 2001 Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies
T. Cabanal Duvillard, A. Guionnet
Ann. Probab. 29(3): 1205-1261 (July 2001). DOI: 10.1214/aop/1015345602

Abstract

Using Itô’s calculus, we study the large deviations properties of the law of the spectral measure of the Hermitian Brownian motion.We extend this strategy to the symmetric, unitary and Wishart processes. This dynamical approach is generalized to the study of the large deviations of the non-commutative laws of several independent Hermitian Brownian motions. As a consequence, we can bound from above entropies defined in the spirit of the microstates entropy introduced by Voiculescu.

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T. Cabanal Duvillard. A. Guionnet. "Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies." Ann. Probab. 29 (3) 1205 - 1261, July 2001. https://doi.org/10.1214/aop/1015345602

Information

Published: July 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1022.60026
MathSciNet: MR1872742
Digital Object Identifier: 10.1214/aop/1015345602

Subjects:
Primary: 15A52 , 60F10
Secondary: 46L50

Keywords: Integration , large deviations , non-commutative measure , random matrices

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.29 • No. 3 • July 2001
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