The pair correlation function of the Sine${}_6$ process

Abstract

We derive an explicit formula for the pair correlation function of the Sine${}_6$ process in terms of Bessel functions of the first kind. This provides the first single-variable special function representation of the pair correlation function for the bulk limit of a beta-ensemble beyond the classical values of $\beta =1,2,$ and $4$.

arXiv comment12 pages, no figures