A note on the run length function for intermittency maps

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 Erdős-Rényi law obtained by Denker and Nicol in \cite{dennic13}.

11 pages, Accepted to Journal of Mathematical Analysis and Applications