Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smallest singular value and limit eigenvalue distribution of a class of
  non-Hermitian random matrices with statistical application   Suppose $X$ is an $N \times n$ complex matrix whose entries are centered,
independent, and identically distributed random variables with variance $1/n$
and whose fourth moment is of order ${\mathcal O}(n^{-2})$. In the first part
of the paper, we consider the non-Hermitian matrix $X A X^* - z$, where $A$ is
a deterministic matrix whose smallest and largest singular values are bounded
below and above respectively, and $z\neq 0$ is a complex number. Asymptotic
probability bounds for the smallest singular value of this model are obtained
in the large dimensional regime where $N$ and $n$ diverge to infinity at the
same rate.
  In the second part of the paper, we consider the special case where $A = J =
[1_{i-j = 1\mod n} ]$ is a circulant matrix. Using the result of the first
part, it is shown that the limit eigenvalue distribution of $X J X^*$ exists in
the large dimensional regime, and we determine this limit explicitly. A
statistical application of this result devoted towards testing the presence of
correlations within a multivariate time series is considered. Assuming that $X$
represents a ${\mathbb C}^N$-valued time series which is observed over a time
window of length $n$, the matrix $X J X^*$ represents the one-step sample
autocovariance matrix of this time series. Guided by the result on the limit
spectral measure of this matrix, a whiteness test against an MA correlation
model on the time series is introduced. Numerical simulations show the
excellent performance of this test.

12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph