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

被引：1
作者：
Ueda, Yuki [1 ]
机构：
[1] Hokkaido Univ, Dept Math, 9 Hokumon Cho, Asahikawa, Hokkaido, Japan
来源：
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2022年 / 25卷 / 03期
关键词：
Free probability theory; free max-convolution; free extreme value distributions; MATRICES;
D O I：
10.1142/S0219025722500199
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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, . . ., X-n. It is known that the renormalized spectral maximum Wn 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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页数：19
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