We study dynamical systems arising as time-dependent compositions of Pomeau-Manneville-type intermittent maps. We establish central limit theorems for appropriately scaled and centered Birkhoff-like partial sums, with estimates on the rate of convergence. For maps chosen from a certain parameter range, but without additional assumptions on how the maps vary with time, we obtain a self-norming CLT provided that the variances of the partial sums grow sufficiently fast. When the maps are chosen randomly according to a shift-invariant probability measure, we identify conditions under which the quenched CLT holds, assuming fiberwise centering. Finally, we show a multivariate CLT for intermittent quasi-static systems. Our approach is based on Stein’s method of normal approximation.

中文翻译：

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时间相关间歇映射的具有收敛速度的中心极限定理

我们研究了作为 Pomeau-Manneville 型间歇地图的时间相关成分而产生的动力系统。我们为适当缩放和居中的类 Birkhoff 部分和建立了中心极限定理，并估计了收敛速度。对于从某个参数范围中选择的地图，但没有关于地图如何随时间变化的额外假设，如果部分和的方差增长足够快，我们将获得自标准化 CLT。当根据移位不变概率测量随机选择映射时，我们确定淬火 CLT 保持的条件，假设纤维居中。最后，我们展示了用于间歇性准静态系统的多元 CLT。我们的方法基于 Stein 的正态近似方法。