Determinantal formulae and loop equations

TL;DR

This paper demonstrates that correlation functions derived from the Christoffel-Darboux kernel of any order 2 ODE satisfy loop equations, establishing a link between determinantal processes and loop equations.

Contribution

It proves that correlation functions from the Christoffel-Darboux kernel of arbitrary order 2 ODE satisfy loop equations, a novel connection in the field.

Findings

Correlation functions satisfy loop equations

Applicability to arbitrary order 2 ODEs

Strengthens link between determinantal processes and loop equations

Abstract

We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations.