Matricial model for the free multiplicative convolution

• Guillaume Cébron ^[1]
  1. [1] Saarland University

     Saarland University

     Regionalverband Saarbrücken, Alemania

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 4, 2016, págs. 2427-2478
• Idioma: inglés
• DOI: 10.1214/15-AOP1024
• Enlaces
  • Texto completo
• Resumen

  • 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 NN limit of a new matricial model on the unitary group for free multiplicative Lévy processes.