Work

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

Year: 2022

Type: article

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.

Source: Infinite Dimensional Analysis Quantum Probability and Related Topics

DOI: 10.1142/s0219025722500199

Author: Yuki Ueda

Institution: Hokkaido University of Education

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

Awards: Limit theorems for diffusions, Levy processes and their variants with their applications, G7433082671