Generating series for GUE correlators

TL;DR

This paper develops a recursive method to generate series for GUE correlators using Toda lattice hierarchy and matrix resolvents, enabling efficient computation of correlators across all genera.

Contribution

It extends the Toda lattice hierarchy approach to compute GUE correlators via matrix resolvents, providing explicit generating series and a recursive computation method.

Findings

Explicit generating series for connected GUE correlators

Efficient recursive procedure for full genus computation

Extension of Toda hierarchy methods to GUE correlators

Abstract

We extend to the Toda lattice hierarchy the approach of [3, 4] to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding differ- ence Lax operator. As a particular application we obtain explicit generating series for connected GUE correlators. On this basis an efficient recursive procedure for computing the correlators in full genera is developed.