Semiclassical expansions in the Toda hierarchy and the hermitian matrix model

TL;DR

This paper develops an iterative algorithm to find solutions of the dispersionful 2-Toda hierarchy related to the Hermitian matrix model, including large N-limit and double scaling limit formulations.

Contribution

It introduces a novel iterative method for solutions of the dispersionful 2-Toda hierarchy linked to matrix models, encompassing large N and double scaling limits.

Findings

Algorithm effectively determines solutions with string equations

Includes the large N-limit of the Hermitian matrix model

Formulates the double scaling limit within the scheme

Abstract

An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix model in the one-cut case. It is also shown how the double scaling limit can be naturally formulated in this scheme