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Rates of convergence for laws of the spectral maximum of free random variables (2105.08258v2)
Published 18 May 2021 in math.PR and math.OA
Abstract: Let ${X_n}_n$ be a sequence of freely independent, identically distributed non-commutative random variables. Consider a sequence ${W_n}_n$ of the renormalized spectral maximum of random variables $X_1,\cdots, X_n$. It is known that the renormalized spectral maximum $W_n$ 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 $W_n$ and the free extreme value distribution.