Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spherical Sherrington-Kirkpatrick model for deformed Wigner matrix with
  fast decaying edges   Consider the deformed Wigner matrix $W+\lambda V$ where $W$ is an $N\times N$
random real symmetric matrix, $\lambda>0$ is a constant and $V$ is an $N\times
N$ random diagonal matrix with iid real-valued entries. Assume that the density
function of the entries of $V$ decays faster than some certain rates near
edges. Suppose $F_N$ is the free energy of the spherical
Sherrington-Kirkpatrick model for $W+\lambda V$ at inverse temperature $\beta$.
Under some technical conditions we prove that there exists a critical value
$\beta_c$ such that:
  1. if $\beta>\beta_c$, then the fluctuation of $F_N$ converges in
distribution to a Weibull distribution as $N\to\infty$;
  2. if $0<\beta<\beta_c$, then the fluctuation of $F_N$ converges in
distribution to a Gaussian distribution as $N\to\infty$.
  As byproducts the following results are obtained for the deformed Wigner
matrix:
  $\quad\bullet$ a local low for resolvent entries;
  $\quad\bullet$ a central limit theorem of the linear statistics;
  $\quad\bullet$ a theorem on the rigidity of eigenvalues.

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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio