Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix

TL;DR

This paper studies the eigenvalue correlations in large multi-matrix models, deriving new asymptotic results and analyzing the limit of an infinite chain as a time-dependent single-matrix model.

Contribution

It introduces new asymptotic formulas for eigenvalue correlations in multi-matrix models and explores the infinite chain limit as a time-dependent matrix model.

Findings

Derived asymptotic expressions for eigenvalue correlations.

Analyzed the infinite chain limit as a time-dependent matrix model.

Provided correlation functions for eigenvalues at different times.

Abstract

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of different matrices of the chain. Eventually, we consider the limit of the infinite chain of matrices, which can be interpreted as a time dependent one-matrix model, and give the correlation functions of eigenvalues at different times.