双间歇映射的淬火混合率
Quenched Mixing Rates for Doubly Intermittent Maps
AI总结：
研究两类含特定奇点区间映射随机组合的淬火混合率，对皮科夫斯基族给出等变样本测度，为格罗斯曼 - 霍纳族构造等变测度族，利用随机杨塔证明有界与赫尔德可观测量纤维相关性的淬火多项式衰减，速率由淬火返回时间尾部估计确定。
摘要：
我们研究了两类区间映射的随机组合的淬火混合率，这两类映射在原点处有两个无差别不动点和一个奇点：皮科夫斯基映射和格罗斯曼 - 霍纳映射。对于皮科夫斯基族，每个纤维映射保持勒贝格测度，等变样本测度由\(\mu_\omega=m\)给出。对于格罗斯曼 - 霍纳族，我们构造了一个绝对连续概率测度的等变族\((\mu_\omega)_{\omega\in\Omega}\)。利用随机杨塔，我们证明了有界可观测量相对于赫尔德可观测量的未来和过去纤维相关性的淬火多项式衰减。这些速率由从随机余圈的端点漂移界获得的淬火返回时间尾部估计确定。
英文摘要：
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 \((μ_ω)_{ω\inΩ}\) 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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