Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of a Fredholm determinant involving the second Painlev\'e
  transcendent   We study the determinant $\det(I-K_{\textnormal{PII}})$ of an integrable
Fredholm operator $K_{\textnormal{PII}}$ acting on the interval $(-s,s)$ whose
kernel is constructed out of the $\Psi$-function associated with the
Hastings-McLeod solution of the second Painlev\'e equation. This Fredholm
determinant describes the critical behavior of the eigenvalue gap probabilities
of a random Hermitian matrix chosen from the Unitary Ensemble in the bulk
double scaling limit near a quadratic zero of the limiting mean eigenvalue
density. Using the Riemann-Hilbert method, we evaluate the large
$s$-asymptotics of $\det(I-K_{\textnormal{PII}})$.

19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys