Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Empirical Processes of Multidimensional Systems with Multiple Mixing
  Properties   We establish a multivariate empirical process central limit theorem for
stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak
conditions concerning the dependence structure of the process. As an
application we can prove the empirical process CLT for ergodic torus
automorphisms. Our results also apply to Markov chains and dynamical systems
having a spectral gap on some Banach space of functions. Our proof uses a
multivariate extension of the techniques introduced by Dehling, Durieu and
Voln\'y \cite{DehDurVol09} in the univariate case. As an important technical
ingredient, we prove a $(2p)$th moment bound for partial sums in multiple
mixing systems.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph