Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large deviation bounds for the Airy point process   In this paper, we establish the first large deviation bounds for the Airy
point process. The proof is based on a novel approach which relies upon the
approximation of the Airy point process using Gaussian unitary ensemble (GUE)
up to exponentially small probability, together with precise estimates for the
stochastic Airy operator and edge rigidity for beta ensembles.
  As a by-product of our estimates for the Airy point process, we significantly
improve upon previous results on the lower tail probability of the one-point
distribution of the KPZ equation with narrow-wedge initial data and the
half-space KPZ equation with Neumann boundary parameter $A=-\frac{1}{2}$ in a
unified and much shorter manner. Our bounds hold for all sufficiently large
time $T$, and for the first time establish sharp super-exponential decay with
exponent $3$ for tail depth less than $T^{\frac{2}{3}}$ (with sharp leading
pre-factors $\frac{1}{12}$ and $\frac{1}{24}$ for tail depth less than $T^{
\frac{1}{6}}$).

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th