论文标题
限制定理用于随机扩展或双曲动力学系统和矢量值可观察的定理
Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables
论文作者
论文摘要
本文的目的是双重的。在一个方向上，我们扩展了光谱方法，以通过第一作者\ textit {et al}开发的随机分段扩展和双曲动力学。为了建立大偏差原理的淬火版本，\ emph {vector-valued}可观测值的中央限制定理和局部中央限制定理。我们强调，以前的作品仅考虑了标量值可观察到的情况。 在另一个方向上，我们表明该方法可用于建立各种新的限制定律（对于标量或矢量值可观测值），这些定律先前尚未在文献中针对我们考虑的动态类别进行讨论。更确切地说，我们建立了中等的偏差原理，浓度不平等，浆果 - 估计以及Edgeworth和大偏差扩展。 尽管我们的技术依赖于第一作者\ textit {et al}的先前作品中开发的方法，但我们强调我们的论点需要几种非平凡的调整以及新想法。
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.
