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July 2016 Matricial model for the free multiplicative convolution
Guillaume Cébron
Ann. Probab. 44(4): 2427-2478 (July 2016). DOI: 10.1214/15-AOP1024

Abstract

This paper investigates homomorphisms à la Bercovici–Pata between additive and multiplicative convolutions. We also consider their matricial versions which are associated with measures on the space of Hermitian matrices and on the unitary group. The previous results combined with a matricial model of Benaych–Georges and Cabanal–Duvillard allow us to define and study the large $N$ limit of a new matricial model on the unitary group for free multiplicative Lévy processes.

Citation

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Guillaume Cébron. "Matricial model for the free multiplicative convolution." Ann. Probab. 44 (4) 2427 - 2478, July 2016. https://doi.org/10.1214/15-AOP1024

Information

Received: 1 February 2014; Revised: 1 March 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 1361.15037
MathSciNet: MR3531672
Digital Object Identifier: 10.1214/15-AOP1024

Subjects:
Primary: 15B52, 60B15
Secondary: 46L54, 60E07

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 4 • July 2016
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