Integrals of tau functions I: Round dance tau function and multi-matrix integrals

TL;DR

This paper explores the relationship between specific tau functions of the Toda lattice and their applications to multi-matrix integrals, highlighting new connections in integrable systems and matrix models.

Contribution

It introduces a novel comparison of tau functions of the Toda lattice and their role in multi-matrix integrals, expanding understanding of integrable systems in mathematical physics.

Findings

Identifies a new class of tau functions relevant to multi-matrix integrals

Establishes connections between Toda lattice tau functions and matrix models

Provides foundational insights for further research in integrable systems

Abstract

The simplest nontrivial tau functions of the Toda lattice and the $\tN$-component Toda lattice are compared in their applications to multimatrix integrals.