# Exponential moments and piecewise thinning for the Bessel point process

## TL;DR

This paper derives exponential moment asymptotics for the Bessel point process, leading to improved expectation and variance estimates, central limit theorems, and insights into large gap behavior and rigidity properties.

## Contribution

It introduces new exponential moment asymptotics for the Bessel point process and connects them to large gap probabilities and global rigidity analysis.

## Key findings

- Improved asymptotics for expectation and variance of the counting function
- Establishment of several central limit theorems
- Interpretation of exponential moments as large gap asymptotics

## Abstract

We obtain exponential moment asymptotics for the Bessel point process. As a direct consequence, we improve on the asymptotics for the expectation and variance of the associated counting function, and establish several central limit theorems. We show that exponential moment asymptotics can also be interpreted as large gap asymptotics, in the case where we apply the operation of a piecewise constant thinning on several consecutive intervals. We believe our results also provide important estimates for later studies of the global rigidity of the Bessel point process.