Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convergence of the extremal eigenvalues of empirical covariance
  matrices with dependence   Consider a sample of a centered random vector with unit covariance matrix. We
show that under certain regularity assumptions, and up to a natural scaling,
the smallest and the largest eigenvalues of the empirical covariance matrix
converge, when the dimension and the sample size both tend to infinity, to the
left and right edges of the Marchenko--Pastur distribution. The assumptions are
related to tails of norms of orthogonal projections. They cover isotropic
log-concave random vectors as well as random vectors with i.i.d. coordinates
with almost optimal moment conditions. The method is a refinement of the rank
one update approach used by Srivastava and Vershynin to produce non-asymptotic
quantitative estimates. In other words we provide a new proof of the Bai and
Yin theorem using basic tools from probability theory and linear algebra,
together with a new extension of this theorem to random matrices with dependent
entries.

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The categories of this paper are: stat
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph