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

Florent Benaych-Georges (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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

Mots clés: free probability; random matrices; free convolution; infinitely divisible laws

Domaines: Probabilités [math.PR]

Florent Benaych-Georges. On a surprising relation between the Marchenko-Pastur law, rectangular and square free convolutions. 2008. ⟨hal-00315507v1⟩