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arXiv · 2312.14581

Local limit theorems for hitting times and return times of small sets

Max Auer·Roland Zweimüller
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Abstract

We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamical systems, including versions for tuples of consecutive times and positions of the hits. These results are shown to apply in the setup of Gibbs-Markov systems.

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Max Auer, Roland Zweimüller. 2023-12-22. Local limit theorems for hitting times and return times of small sets. https://arxiv.org/abs/2312.14581

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