Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detection of weak signals in high-dimensional complex-valued data   This paper considers the problem of detecting a few signals in
high-dimensional complex-valued Gaussian data satisfying Johnstone's (2001)
\textit{spiked covariance model}. We focus on the difficult case where signals
are weak in the sense that the sizes of the corresponding covariance spikes are
below the \textit{phase transition threshold} studied in Baik et al (2005). We
derive a simple analytical expression for the maximal possible asymptotic
probability of correct detection holding the asymptotic probability of false
detection fixed. To accomplish this derivation, we establish what we believe to
be a new formula for the \textit{% Harish-Chandra/Itzykson-Zuber (HCIZ)
integral} $\int_{\mathcal{U}(p)}e^{\tr(AGBG^{-1})}dG $, where $A$ has a
deficient rank $r<p$. The formula links the HCIZ integral over $\mathcal{U}(p)
$ to an HCIZ integral over a potentially much smaller unitary group
$\mathcal{U}(r) $. We show that the formula generalizes to the integrals over
orthogonal and symplectic groups. In the most general form, it expresses the
hypergeometric function $_{0}F_{0}^{(\alpha)}$of two $p\times p$ matrix
arguments as a repeated contour integral of the hypergeometric function
$_{0}F_{0}^{(\alpha)}$of two $r\times r$ matrix arguments.

3
The categories of this paper are: physics
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex