A matrix interpolation between classical and free max operations: I. The univariate case

Florent Benaych-Georges (1) , Thierry Cabanal-Duvillard (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy, based on random matrices giving an interpolation between classical and free settings.

Mots clés: random matrices; free probability; max-stable laws; extreme values

Domaines: Probabilités [math.PR]

Florent Benaych-Georges, Thierry Cabanal-Duvillard. A matrix interpolation between classical and free max operations: I. The univariate case. 2008. ⟨hal-00289807v1⟩