Large deviation bounds for the Airy point process

Chenyang Zhong

Published 2019-10-02Version 1

In this paper, we establish large deviation bounds for the Airy point process. Specifically, we establish exponential tightness, large deviation lower bound and large deviation upper bound for "nice tubes" (with definition in the main text). The proof is based on the approximation of the Airy point process using Gaussian unitary ensemble (GUE) up to exponentially small probability. To establish the corresponding large deviation bounds for GUE, we refine some edge rigidity results up to tail probabilities, and establish some estimates for the diffusion associated with the stochastic Airy operator.