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arXiv · 2105.08258

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

Yuki Ueda
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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.

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Yuki Ueda. 2021-05-18. Rates of convergence for laws of the spectral maximum of free random variables. https://arxiv.org/abs/2105.08258

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