Rates of convergence for laws of the spectral maximum of free random variables

Abstract

Let [Formula: see text] be a sequence of freely independent, identically distributed non-commutative random variables. Consider a sequence [Formula: see text] of the renormalized spectral maximum of random variables [Formula: see text]. It is known that the renormalized spectral maximum [Formula: see text] converges to the free extreme value distribution under certain conditions on the distribution function. In this paper, we provide a rate of convergence in the Kolmogorov distance between a distribution function of [Formula: see text] and the free extreme value distribution.