Large N asymptotics of orthogonal polynomials, from integrability to algebraic geometry

TL;DR

This paper explores the asymptotic behavior of orthogonal polynomials using saddle point methods, highlighting connections between integrability, algebraic geometry, and random matrix theory.

Contribution

It demonstrates a method to compute orthogonal polynomial asymptotics, bridging integrability and algebraic geometry in the context of random matrices.

Findings

Asymptotic formulas for orthogonal polynomials derived

Link established between integrability, algebraic geometry, and random matrices

Illustrates saddle point approximation in this setting

Abstract

In this short lecture, we compute asymptotics of orthogonal polynomials, from a saddle point approximation. This is an example of a calculation which shows the link between integrability, algebraic geometry and random matrices.