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Determinantal structures for Bessel fields
- Publication Year :
- 2021
-
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.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2109.09292
- Document Type :
- Working Paper