Quenched Mixing Rates for Doubly Intermittent Maps

2024/04/15 by Mubarak Muhammad, Muhammad, Mubarak, Marks Ruziboev +1 · 2 citations
Mathematics · #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.DS

paper · pdf · doi:10.48550/arxiv.2404.09751

openalex publication_date 2024/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We study quenched mixing rates for random compositions of two classes of interval maps with two indifferent fixed points and a singularity at the origin: Pikovsky maps and Grossmann--Horner maps. For the Pikovsky family, each fibre map preserves Lebesgue measure, so the equivariant sample measures are given by \(μ_ω=m\). For the Grossmann--Horner family, we construct an equivariant family \((μ_ω)_ω∈Ω\) of absolutely continuous probability measures. Using random Young towers, we prove quenched polynomial decay of both future and past fibre correlations for bounded observables against Hölder observables. The rates are determined by quenched return time tail estimates obtained from endpoint drift bounds for the random cocycle.

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• Decay of correlations and limit theorems for random intermittent maps
• Quenched invariance principle with a rate for random dynamical systems

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