Gap probabilities in the bulk of the Airy process

TL;DR

This paper investigates the probability of no points in large intervals within the bulk of the Airy process, proposing a detailed asymptotic conjecture and proving it for a single interval.

Contribution

It introduces a conjecture for the full asymptotic expansion of gap probabilities in the Airy process and proves it for the case of one interval.

Findings

Conjectured asymptotics include oscillatory terms of order 1.

Proved the conjecture for the case of a single interval.

Provides a framework for understanding gap probabilities in the Airy process.

Abstract

We consider the probability that no points lie on $g$ large intervals in the bulk of the Airy point process. We make a conjecture for all the terms in the asymptotics up to and including the oscillations of order $1$, and we prove this conjecture for $g=1$.