Quenched Mixing Rates for Doubly Intermittent Maps

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 \(\mu_\omega=m\). For the Grossmann--Horner family, we construct an equivariant family \((\mu_\omega)_{\omega\in\Omega}\) 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 H\"older observables. The rates are determined by quenched return time tail estimates obtained from endpoint drift bounds for the random cocycle.