Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On complex Gaussian random fields, Gaussian quadratic forms and sample
  distance multivariance   The paper contains results in three areas: First we present a general
estimate for tail probabilities of Gaussian quadratic forms with known
expectation and variance. Thereafter we analyze the distribution of norms of
complex Gaussian random fields (with possibly dependent real and complex part)
and derive representation results, which allow to find efficient estimators for
the moments of the associated Gaussian quadratic form. Finally, we apply these
results to sample distance multivariance, which is the test statistic
corresponding to distance multivariance -- a recently introduced multivariate
dependence measure. The results yield new tests for independence of multiple
random vectors. These are less conservative than the classical tests based on a
general quadratic form estimate and they are (much) faster than tests based on
a resampling approach. As a special case this also improves independence tests
based on distance covariance, i.e., tests for independence of two random
vectors.

36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat