Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large deviations, moment estimates and almost sure invariance principles
  for skew products with mixing base maps and expanding on the average fibers   In this paper we show how to apply classical probabilistic tools for partial
sums $\sum_{j=0}^{n-1}\varphi\circ\tau^j$ generated by a skew product $\tau$,
built over a sufficiently well mixing base map and a random expanding dynamical
system. Under certain regularity assumptions on the observable $\varphi$, we
obtain a central limit theorem (CLT) with rates, a functional CLT, an almost
sure invariance principle (ASIP), a moderate deviations principle, several
exponential concentration inequalities and Rosenthal type moment estimates for
skew products with $\alpha, \phi$ or $\psi$ mixing base maps and expanding on
the average random fiber maps. All of the results are new even in the uniformly
expanding case. The main novelty here (contrary to \cite{ANV}) is that the
random maps are not independent, they do not preserve the same measure and the
observable $\varphi$ depends also on the base space. For stretched
exponentially $\al$-mixing base maps our proofs are based on multiple
correlation estimates, which make the classical method of cumulants applicable.
  For $\phi$ or $\psi$ mixing base maps, we obtain an ASIP and maximal and
concentration inequalities by establishing an $L^\infty$ convergence of the
iterates $\cK^n$ of a certain transfer operator $\cK$ with respect to a certain
sub-$\sig$-algebra, which yields an appropriate (reverse) martingale-coboundary
decomposition.

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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph