Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies

Large Deviations Upper Bounds for the Laws of Matrix-Valued Processes and Non-Communicative Entropies

T. Cabanal Duvillard and A. Guionnet

Source: Ann. Probab. Volume 29, Number 3 (2001), 1205-1261.

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.

Primary Subjects: 60F10, 15A52

Secondary Subjects: 46L50

Keywords: Large deviations; random matrices; non-commutative measure; integration

Full-text: Open access

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Permanent link to this document: http://projecteuclid.org/euclid.aop/1015345602
Digital Object Identifier: doi:10.1214/aop/1015345602
Mathematical Reviews number (MathSciNet): MR1872742

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