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arXiv · 2401.08802

Rates of convergence in CLT and ASIP for sequences of expanding maps

Dmitry Dolgopyat·Yeor Hafouta
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Abstract

We prove Berry-Esseen theorems and the almost sure invariance principle with rates for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j\circ T_{j-1}\circ\cdots\circ T_1\circ T_0$ where $f_j$ are functions with uniformly bounded ``variation" and $T_j$ is a sequence of expanding maps. Using symbolic representations similar result follow for maps $T_j$ in a small $C^1$ neighborhood of an Axiom A map and H\"older continuous functions $f_j$. All of our results are already new for a single map $T_j=T$ and a sequence of different functions $(f_j)$.

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Dmitry Dolgopyat, Yeor Hafouta. 2024-01-16. Rates of convergence in CLT and ASIP for sequences of expanding maps. https://arxiv.org/abs/2401.08802

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