Orthogonal polynomial method and odd vertices in matrix models

TL;DR

This paper introduces an orthogonal polynomial approach to compute the partition function of one-matrix models with potentials containing even and odd vertices in the planar approximation.

Contribution

It extends the orthogonal polynomial method to handle matrix models with mixed even and odd vertex potentials in the planar limit.

Findings

Successfully applies the method to models with mixed vertex types.

Provides a framework for integrating partition functions with complex potentials.

Enhances analytical tools for matrix model analysis.

Abstract

We show how to use the method of orthogonal polynomials for integrating, in the planar approximation, the partition function of one-matrix models with a potential with even or odd vertices, or any combination of them.