We prove a Berry–Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain random (Young) tower extensions, which is the main focus of this paper. On the random towers we will obtain our results using contraction properties of random complex equivariant cones with respect to the complex Hilbert projective metric.

中文翻译：

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具有指数尾部的随机非均匀扩展或双曲映射的极限定理

我们证明了 Berry-Esseen 定理、局部中心极限定理和（局部）大和（全局）中等偏差原则，用于具有指数首次返回时间的 iid（均匀）随机非均匀扩展或双曲线映射。使用现有结果将问题简化为某些随机（年轻）塔扩展，这是本文的主要重点。在随机塔上，我们将使用随机复等变锥相对于复 Hilbert 投影度量的收缩特性来获得我们的结果。