Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tail decay for the distribution of the endpoint of a directed polymer   We obtain an asymptotic expansion for the tails of the random variable
$\tcal=\arg\max_{u\in\mathbb{R}}(\mathcal{A}_2(u)-u^2)$ where $\mathcal{A}_2$
is the Airy$_2$ process. Using the formula of Schehr \cite{Sch} that connects
the density function of $\tcal$ to the Hastings-McLeod solution of the second
Painlev\'e equation, we prove that as $t\rightarrow\infty$,
$\mathbb{P}(|\tcal|>t)=Ce^{-4/3\varphi(t)}t^{-145/32}(1+O(t^{-3/4}))$, where
$\varphi(t)=t^3-2t^{3/2}+3t^{3/4}$, and the constant $C$ is given explicitly.

11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys