Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Limiting Empirical Measure of the sum of rank one matrices with
  log-concave distribution   We consider $n\times n$ real symmetric and hermitian random matrices
$H_{n,m}$ equals the sum of a non-random matrix $H_{n}^{(0)}$ matrix and the
sum of $m$ rank-one matrices determined by $m$ i.i.d. isotropic random vectors
with log-concave probability law and i.i.d. random amplitudes $\{\tau_{\alpha
}\}_{\alpha =1}^{m}$. This is a generalization of the case of vectors uniformly
distributed over the unit sphere, studied in [Marchenko-Pastur (1967)]. We
prove that if $n\to \infty, m\to \infty, m/n\to c\in \lbrack 0,\infty)$ and
that the empirical eigenvalue measure of $H_{n}^{(0)}$ converges weakly, then
the empirical eigenvalue measure of $H_{n,m}$ converges in probability to a
non-random limit, found in [Marchenko-Pastur (1967)].

10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th