Double Scaling Limit in Random Matrix Models and a Nonlinear Hierarchy of Differential Equations

TL;DR

This paper investigates the double scaling limit in random matrix models at critical points, linking the resulting eigenvalue correlations to a hierarchy of nonlinear differential equations.

Contribution

It introduces a novel connection between the double scaling limit of eigenvalue correlations and a hierarchy of nonlinear ODEs in random matrix theory.

Findings

Derived the double scaling limit of eigenvalue correlations.

Established a relationship with a hierarchy of nonlinear differential equations.

Provided new insights into critical phenomena in random matrices.

Abstract

We derive the double scaling limit of eigenvalue correlations in the random matrix model at critical points and we relate the limiting correlation functions to a nonlinear hierarchy of ordinary differential equations.