Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A CLT for Information-theoretic statistics of Gram random matrices with
  a given variance profile   Consider a $N\times n$ random matrix $Y_n=(Y_{ij}^{n})$ where the entries are
given by $$ Y_{ij}^{n}=\frac{\sigma_{ij}(n)}{\sqrt{n}} X_{ij}^{n} $$ the
$X_{ij}^{n}$ being centered, independent and identically distributed random
variables with unit variance and $(\sigma_{ij}(n); 1\le i\le N, 1\le j\le n)$
being an array of numbers we shall refer to as a variance profile. We study in
this article the fluctuations of the random variable $$ \log\det(Y_n Y_n^* +
\rho I_N) $$ where $Y^*$ is the Hermitian adjoint of $Y$ and $\rho > 0$ is an
additional parameter. We prove that when centered and properly rescaled, this
random variable satisfies a Central Limit Theorem (CLT) and has a Gaussian
limit whose parameters are identified. A complete description of the scaling
parameter is given; in particular it is shown that an additional term appears
in this parameter in the case where the 4$^\textrm{th}$ moment of the
$X_{ij}$'s differs from the 4$^{\textrm{th}}$ moment of a Gaussian random
variable. Such a CLT is of interest in the field of wireless communications.

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The categories of this paper are: solv-int
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom