probability theory

The pair correlation function of the Sine process

arXiv:2607.26223

summary

The paper derives an explicit formula for the pair correlation function of the Sine_6 process, expressing it in terms of Bessel functions of the first kind, extending known results beyond the classical beta values 1, 2, and 4.

Abstract

We derive an explicit formula for the pair correlation function of the Sine 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 and .

12 pages, no figures

Topics & keywords

#random matrix theory#beta-ensembles#pair correlation function#sine process#special functionsSine_6 processpair correlation functionBessel functionsbeta-ensemblebulk limit
The pair correlation function of the Sine$_6$ process · wovepaper