We obtain large and moderate deviation estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems obtained by Nicol, Török and Vaienti [Central limit theorems for sequential and random intermittent dynamical systems. Ergod. Th. & Dynam. Sys.38(3) (2018), 1127–1153] for random dynamical systems comprising intermittent maps. Using recent work of Abdelkader and Aimino [On the quenched central limit theorem for random dynamical systems. J. Phys. A 49(24) (2016), 244002] and Hella and Stenlund [Quenched normal approximation for random sequences of transformations. J. Stat. Phys.178(1) (2020), 1–37] we extend the results of Nicol, Török and Vaienti on quenched central limit theorems for centered observables over random compositions of intermittent maps: first by enlarging the parameter range over which the quenched central limit theorem holds; and second by showing that the variance in the quenched central limit theorem is almost surely constant (and the same as the variance of the annealed central limit theorem) and that centering is needed to obtain this quenched central limit theorem.

中文翻译：

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间歇映射序列和随机系统的大偏差和中心极限定理

我们获得了间歇性地图的连续和随机组合的大和中度偏差估计。我们还解决了 Nicol、Török 和 Vaienti 获得的淬火中心极限定理是否需要居中的问题[连续和随机间歇动力系统的中心极限定理。埃尔戈德。钍。&动态。系统。38(3) (2018), 1127–1153] 用于包含间歇映射的随机动力系统。使用 Abdelkader 和 Aimino 最近的工作 [关于随机动力系统的淬火中心极限定理。J.物理。一种49(24) (2016), 244002] 和 Hella 和 Stenlund [用于随机变换序列的淬火正态近似。J.统计。物理。178(1) (2020), 1-37] 我们扩展了 Nicol、Török 和 Vaienti 关于在间歇映射的随机组合上的中心可观测量的淬火中心极限定理的结果：首先通过扩大淬火中心极限定理所适用的参数范围; 其次，通过证明淬火中心极限定理的方差几乎肯定是恒定的（并且与退火中心极限定理的方差相同），并且需要中心化来获得这个淬火中心极限定理。