Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps

2025/03/20 by Fleming-Vázquez, Nicholas · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.16358

Abstract

We obtain rates of convergence in the weak invariance principle (functional central limit theorem) for \R^d-valued Hölder observables of nonuniformly hyperbolic maps. In particular, for maps modelled by a Young tower with superpolynomial tails (e.g. the Sinai billiard map, and Axiom A diffeomorphisms) we obtain a rate of O(n^-κ) in the Wasserstein p-metric for all κ<1/4 and p<∞. Additionally, this is the first result on rates that covers certain invertible, slowly mixing maps, such as Bunimovich flowers.

Cited by

• Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
• Quenched invariance principle with a rate for random dynamical systems

Related

• Wasserstein convergence rates in the invariance principle for deterministic dynamical systems
• Wasserstein convergence rates in the invariance principle for nonuniformly hyperbolic flows
• Rates in almost sure invariance principle for nonuniformly hyperbolic maps
• Rates for maps and flows in a deterministic multidimensional weak invariance principle
• Nonstandard functional central limit theorem for nonuniformly hyperbolic dynamical systems, including Bunimovich stadia