A matrix interpolation between classical and free max operations: I. The univariate case

TL;DR

This paper introduces a matrix interpolation method that bridges classical and free maximum operations, providing a new perspective on the analogy between free probability and classical probability through random matrix models.

Contribution

It offers a novel matrix-based interpolation between classical and free max operations, deepening understanding of their relationship in probability theory.

Findings

Provides a concrete matrix interpolation model

Establishes a new connection between classical and free max operations

Enhances understanding of free probability through random matrices

Abstract

Recently, Ben Arous and Voiculescu considered taking the maximum of two free random variables and brought to light a deep analogy with the operation of taking the maximum of two independent random variables. We present here a new insight on this analogy: its concrete realization based on random matrices giving an interpolation between classical and free settings.