The Annals of Probability

Matricial model for the free multiplicative convolution

Guillaume Cébron

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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.

Article information

Source
Ann. Probab., Volume 44, Number 4 (2016), 2427-2478.

Dates
Received: February 2014
Revised: March 2015
First available in Project Euclid: 2 August 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1470139146

Digital Object Identifier
doi:10.1214/15-AOP1024

Mathematical Reviews number (MathSciNet)
MR3531672

Zentralblatt MATH identifier
1361.15037

Subjects
Primary: 15B52: Random matrices 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 46L54: Free probability and free operator algebras 60E07: Infinitely divisible distributions; stable distributions

Keywords
Random matrices free probability infinitely divisible distributions

Citation

Cébron, Guillaume. Matricial model for the free multiplicative convolution. Ann. Probab. 44 (2016), no. 4, 2427--2478. doi:10.1214/15-AOP1024. https://projecteuclid.org/euclid.aop/1470139146


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