Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The density of eigenvalues seen from the soft edge of random matrices in
  the Gaussian beta-ensembles   We characterize the phenomenon of "crowding" near the largest eigenvalue
$\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian
$\beta$-ensemble of random matrix theory, including in particular the Gaussian
orthogonal ($\beta=1$), unitary ($\beta=2$) and symplectic ($\beta = 4$)
ensembles. We focus on two distinct quantities: (i) the density of states (DOS)
near $\lambda_{\max}$, $\rho_{\rm DOS}(r,N)$, which is the average density of
eigenvalues located at a distance $r$ from $\lambda_{\max}$ (or the density of
eigenvalues seen from $\lambda_{\max}$) and (ii) the probability density
function of the gap between the first two largest eigenvalues, $p_{\rm
GAP}(r,N)$. Using heuristic arguments as well as well numerical simulations, we
generalize our recent exact analytical study of the Hermitian case
(corresponding to $\beta = 2$). We also discuss some applications of these two
quantities to statistical physics models.

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The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
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The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat