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arXiv · 2003.03631

Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables

Davor Dragičević·Yeor Hafouta
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Abstract

The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation principle, central limit theorem and the local central limit theorem for \emph{vector-valued} observables. We stress that the previous works considered exclusively the case of scalar-valued observables. In another direction, we show that this method can be used to establish a variety of new limit laws (either for scalar or vector-valued observables) that have not been discussed previously in the literature for the classes of dynamics we consider. More precisely, we establish the moderate deviation principle, concentration inequalities, Berry-Esseen estimates as well as Edgeworth and large deviation expansions. Although our techniques rely on the approach developed in the previous works of the first author \textit{et al}., we emphasize that our arguments require several nontrivial adjustments as well as new ideas.

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Davor Dragičević, Yeor Hafouta. 2020-03-07. Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables. https://doi.org/10.1007/s00023-020-00965-7

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