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arXiv · 2509.04740

On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems

Jonathan DeWitt·Dmitry Dolgopyat
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Abstract

In this paper, we prove several theorems relating annealed exponential mixing of the two-point motion with quenched properties of the one-point motion for conservative IID random dynamical systems. In particular, we show that annealed exponential mixing of the two-point motion implies quenched exponential mixing of the one-point motion. We also show that if the two-point motion satisfies annealed exponential mixing and the annealed central limit theorem with polynomial rate of convergence, then the one-point motion satisfies a quenched CLT. These results hold for all H\"older and Sobolev spaces of positive index.

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Jonathan DeWitt, Dmitry Dolgopyat. 2025-09-05. On equivalence of quenched and annealed statistical properties for conservative IID random dynamical systems. https://arxiv.org/abs/2509.04740

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