Determinantal structures for Bessel fields

Abstract

A Bessel field $\mathcal{B}=\{\mathcal{B}(\alpha ,t),\alpha \in {\mathbb{N}}_0,t\in \mathbb{R}\}$ is a two-variable random field such that for every $(\alpha ,t)$, $\mathcal{B}(\alpha ,t)$ has the law of a Bessel point process with index $\alpha$. The Bessel fields arise as hard edge scaling limits of the Laguerre field, a natural extension of the classical Laguerre unitary ensemble. It is recently proved in [LW21] that for fixed $\alpha$, $\{\mathcal{B}(\alpha ,t),t\in \mathbb{R}\}$ is a squared Bessel Gibbsian line ensemble. In this paper, we discover rich integrable structures for the Bessel fields: along a time-like or a space-like path, $\mathcal{B}$ is a determinantal point process with an explicit correlation kernel; for fixed $t$, $\{\mathcal{B}(\alpha ,t),\alpha \in {\mathbb{N}}_0\}$ is an exponential Gibbsian line ensemble.