Rectangular random matrices. Related convolution

Florent Benaych-Georges (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are asymtotically free with amalgamation over a subalgebra. Therefore we can define a "rectangular free convolution", linearized by cumulants and by an analytic integral transform, called the "rectangular R-transform".

Mots clés: random matrices; free probability; free convolution

Domaines: Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Florent Benaych-Georges. Rectangular random matrices. Related convolution. 2008. ⟨hal-00007541v6⟩