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

2025/09/05 by Jonathan DeWitt, Dmitry Dolgopyat, DeWitt, Jonathan +1 · 1 citation
Physics and Astronomy · #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2509.04740

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 Hölder and Sobolev spaces of positive index.

Citations

• Conservative Coexpanding on Average Diffeomorphisms
• Expanding on average diffeomorphisms of surfaces: exponential mixing
• Limit theorems for low dimensional generalized (T,T^-1) transformations
• Flexibility of statistical properties for smooth systems satisfying the central limit theorem
• Mixing properties of generalized T, T^-1 transformations
• Decay of correlations for certain isometric extensions of Anosov flows
• On the relation between enhanced dissipation time-scales and mixing\n rates
• Central Limit Theorems for group actions which are exponentially mixing\n of all orders
• Sample path properties of the stochastic flows
• Almost sure invariance principles for partial sums of weakly dependent random variables

Cited by

• Mixing at the Batchelor Scale for White-In-Time Flows

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