Quenched invariance principle with a rate for random dynamical systems

2025/06/16 by Zhenxin Liu, Liu, Zhenxin, Benoît Saussol +5 · 1 citation
Mathematics · Physics and Astronomy · #37A50 #37H30 #60B10 #60F17 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2506.13167

openalex publication_date 2025/06/16 · openalex created_date 2025/10/07 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the quenched invariance principle for random Young towers driven by an ergodic system. In particular, we obtain the Wassertein convergence rate in the quenched invariance principle. As a key ingredient, we derive a new martingale-coboundary decomposition for the random tower map, which provides a good control over sums of squares of the approximating martingale. We apply our results to a class of random dynamical systems that admit a random Young tower, such as independent and identically distributed (i.i.d.) translations of Viana maps, intermittent maps of the interval and small random perturbations of Anosov maps with an ergodic driving system.

Citations

• Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps
• Rates for maps and flows in a deterministic multidimensional weak invariance principle
• Quenched Mixing Rates for Doubly Intermittent Maps
• Wasserstein convergence rates in the invariance principle for sequential dynamical systems
• Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems
• Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps
• Wasserstein convergence rates in the invariance principle for deterministic dynamical systems
• Limit theorems for random non-uniformly expanding or hyperbolic maps\n with exponential tails
• Almost sure invariance principle for random dynamical systems via\n Gou "ezel 's approach
• Almost sure rates of mixing for partially hyperbolic attractors
• A spectral approach for quenched limit theorems for random hyperbolic dynamical systems
• Quenched decay of correlations for slowly mixing systems
• Almost sure mixing rates for non-uniformly expanding maps
• Strong stochastic stability for non-uniformly expanding maps
• Recurrence times and rates of mixing
• Statistical Properties of Dynamical Systems with Some Hyperbolicity

Cited by

• Decay of correlations and limit theorems for random intermittent maps

Related

• Random Young Towers and Quenched Limit Laws
• Iterated invariance principle for random dynamical systems
• Almost sure invariance principle for random dynamical systems via\n Gou "ezel 's approach
• Random dynamical systems
• Quenched Invariance Principles via Martingale Approximation