Almost sure rates of mixing for random intermittent maps

Abstract

We consider a family $\mathcal{F}$ of maps with two branches and a common neutral fixed point $0$ such that the order of tangency at $0$ belongs to some interval $[{\alpha }_0,{\alpha }_1]\subset (0,1)$. Maps in $\mathcal{F}$ do not necessarily share a common Markov partition. At each step a member of $\mathcal{F}$ is chosen independently with respect to the uniform distribution on $[{\alpha }_0,{\alpha }_1]$. We show that the construction of the random tower in Bahsoun-Bose-Ruziboev \cite{BBR} with \emph{general return time} can be carried out for random compositions of such maps. Thus their general results are applicable and gives upper bounds for the quenched decay of correlations of form $n^{1-1/{\alpha }_0+\delta }$ for any $\delta >0$.

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