Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large random matrix approach for testing independence of a large number
  of Gaussian time series   The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed
periodogram estimator of the spectral coherency matrix of a complex Gaussian
high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent
components is studied under the asymptotic regime where the sample size $N$
converges towards $+\infty$ while the dimension $M$ of $\y$ and the smoothing
span of the estimator grow to infinity at the same rate in such a way that
$\frac{M}{N} \rightarrow 0$. It is established that, at each frequency, the
estimated spectral coherency matrix is close from the sample covariance matrix
of an independent identically $\mathcal{N}_{\mathbb{C}}(0,\I_M)$ distributed
sequence, and that its empirical eigenvalue distribution converges towards the
Marcenko-Pastur distribution. This allows to conclude that each LSS has a
deterministic behaviour that can be evaluated explicitly. Using concentration
inequalities, it is shown that the order of magnitude of the supremum over the
frequencies of the deviation of each LSS from its deterministic approximation
is of the order of $\frac{1}{M} + \frac{\sqrt{M}}{N}+ (\frac{M}{N})^{3}$ where
$N$ is the sample size. Numerical simulations supports our results.

11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org