Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-dimensional sample covariance matrices with Curie-Weiss entries   We study the limiting spectral distribution of sample covariance matrices
$XX^T$, where $X$ are $p\times n$ random matrices with correlated entries, for
the cases $p/n\to y\in [0,\infty)$. If $y>0$, we obtain the Mar\v{c}enko-Pastur
distribution and in the case $y=0$ the semicircle distribution (after
appropriate rescaling). The entries we consider are Curie-Weiss spins, which
are correlated random signs, where the degree of the correlation is governed by
an inverse temperature $\beta>0$. The model exhibits a phase transition at
$\beta=1$. The correlation between any two entries decays at a rate of $O(np)$
for $\beta \in (0,1)$, $O(\sqrt{np}$) for $\beta=1$, and for $\beta>1$ the
correlation does not vanish in the limit. In our proofs we use Stieltjes
transforms and concentration of random quadratic forms.

16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: cond-mat