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arXiv · 1806.09363

A note on the run length function for intermittency maps

Hongfei Cui·Lulu Fang·Yiwei Zhang
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Abstract

We study the run length function for intermittency maps. In particular, we show that the longest consecutive zero digits (resp. one digits) having a time window of polynomial (resp. logarithmic) length. Our proof is relatively elementary in the sense that it only relies on the classical Borel-Cantelli lemma and the polynomial decay of intermittency maps. Our results are compensational to the Erd\H{o}s-R\'{e}nyi law obtained by Denker and Nicol in \cite{dennic13}.

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Hongfei Cui, Lulu Fang, Yiwei Zhang. 2018-06-25. A note on the run length function for intermittency maps. https://doi.org/10.1016/j.jmaa.2018.11.058

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