On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2010

On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions

Résumé

In this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko-Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.

Dates et versions

hal-00518147 , version 1 (16-09-2010)

Identifiants

Citer

F. Benaych-Georges. On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2010, 46 (3), pp.644-652. ⟨10.1214/09-AIHP324⟩. ⟨hal-00518147⟩
23 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More