Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Behaviour of the Number of Minima of a Random Landscape at the
  Glass Transition Point and the Tracy-Widom distribution   We exploit a relation between the mean number $N_{m}$ of minima of random
Gaussian surfaces and extreme eigenvalues of random matrices to understand the
critical behaviour of $N_{m}$ in the simplest glass-like transition occuring in
a toy model of a single particle in $N$-dimensional random environment, with
$N\gg 1$. Varying the control parameter $\mu$ through the critical value
$\mu_c$ we analyse in detail how $N_{m}(\mu)$ drops from being exponentially
large in the glassy phase to $N_{m}(\mu)\sim 1$ on the other side of the
transition. We also extract a subleading behaviour of $N_{m}(\mu)$ in both
glassy and simple phases. The width $\delta{\mu}/\mu_c$ of the critical region
is found to scale as $N^{-1/3}$ and inside that region $N_{m}(\mu)$ converges
to a limiting shape expressed in terms of the Tracy-Widom distribution.

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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex