Random matrices with external source and KP $\tau$ functions

TL;DR

This paper proves that the partition function of a random matrix model with an external source can be represented as a KP tau function, linking random matrix theory with integrable systems.

Contribution

It establishes a novel connection between random matrix models with external sources and KP tau functions, expanding the understanding of their mathematical structure.

Findings

Partition function is a KP tau function.

Links random matrix models to integrable systems.

Provides a new analytical framework for external source models.

Abstract

In this paper we prove that the partition function in the random matrix model with external source is a KP $\tau$ function.