Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Levy-Khintchine random matrices and the Poisson weighted infinite
  skeleton tree   We study a class of Hermitian random matrices which includes and generalizes
Wigner matrices, heavy-tailed random matrices, and sparse random matrices such
as the adjacency matrices of Erdos-Renyi random graphs with p ~ 1/N. Our NxN
random matrices have real entries which are i.i.d. up to symmetry. The
distributions may depend on N, however, the sums of rows must converge in
distribution; it is then well-known that the limiting distributions are
infinitely divisible.
  We show that a limiting empirical spectral distribution (LSD) exists, and via
local weak convergence of associated graphs, the LSD corresponds to the
spectral measure at the root of a Poisson weighted infinite skeleton tree. This
graph is formed by connecting infinitely many Poisson weighted infinite trees
using a backbone structure. One example covered by the results are matrices
with i.i.d. entries having infinite second moments, but normalized to be in the
Gaussian domain of attraction. In this case, the limiting graph is just the
positive integer line rooted at 1, and as expected, the LSD is Wigner's
semi-circle law. The results also extend to self-adjoint complex matrices and
also to Wishart matrices.

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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat