A note on convergence of densities to free extreme value distributions

TL;DR

This paper investigates the convergence of densities to free extreme value distributions in the context of free probability, extending the understanding of spectral maxima of free noncommutative variables under specific conditions.

Contribution

It provides new results on the convergence of densities to free extreme value distributions under the von Mises condition.

Findings

Convergence of densities established under von Mises condition

Extension of free extreme value theory to density convergence

Insights into spectral maxima of free noncommutative variables

Abstract

The concept of free extreme value distributions as universal limit laws for the spectral maximum of free noncommutative real random variables was discovered by Ben Arous and Voiculescu in 2006. This paper contributes to study the convergence of densities towards free extreme value distributions under the von Mises condition for sample distributions.