非平衡态热力学形式主义 第三部分：局部极限定理与统计性质
Thermodynamic Formalism Out of Equilibrium Part III: Local Limit Theorem and Statistical Properties
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中文总结 AI 辅助
本研究通过Varadhan技巧和算子谱方法，证明了随机动力系统的一系列统计性质，首次在广泛无限制条件下建立了局部极限定理。
中文摘要 AI 辅助
我们研究随机动力系统的极限定理。我们通过两点运动的斜积（Varadhan技巧）重新构造随机动力学。利用这种方法，我们证明了系统的若干统计性质，包括带速率的淬火中心极限定理、淬火局部极限定理、大偏差以及相关性衰减。然后，在应用中，我们展示了如何利用适当算子的谱性质来验证一般条件。一个关键应用是研究平均有效扩张的随机微分同胚（在任意维度中，允许耗散）。特别是，这是在不施加动力学限制的如此广泛背景下首次证明局部极限定理。我们提供了几个新例子。
英文摘要
We study limit theorems for random dynamical systems. We recast the random dynamics via the skew-product of the two-point motion (the Varadhan trick). Using this approach we prove several statistical properties for the system, including quenched central limit theorems with rates, quenched local limit theorem, large deviations, and decay of correlations. Then, in applications we show how to verify the general conditions using spectral properties of appropriate operators. A key application is the study of effectively expanding on average random diffeomorphisms (in any dimension, which are allowed to be dissipative). In particular, this is the first instance of proving local limit theorems in such a broad setting, without imposing restrictions on the dynamics. We provide several new examples.
