A universality theorem for ratios of random characteristic polynomials

TL;DR

This paper proves a universality theorem for the asymptotic behavior of ratios of random characteristic polynomials in orthogonal polynomial ensembles, showing that these ratios exhibit universal limits under broad conditions.

Contribution

It establishes a new universality limit for ratios of characteristic polynomials in orthogonal polynomial ensembles, expanding understanding of their asymptotic behavior.

Findings

Universality limit for ratios of characteristic polynomials

Applicable under broad conditions on the measure

Advances theoretical understanding of orthogonal polynomial ensembles

Abstract

We consider asymptotics of ratios of random characteristic polynomials associated with orthogonal polynomial ensembles. Under some natural conditions on the measure in the definition of the orthogonal polynomial ensemble we establish a universality limit for these ratios.