Abstract:We obtain rates of convergence in the weak invariance principle (functional central limit theorem) for $\mathbb{R}^d$-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 $O(n^{-\kappa})$ in the Wasserstein $p$-metric for all $\kappa<1/4$ and $p<\infty$. Additionally, this is the first result on rates that covers certain invertible, slowly mixing maps, such as Bunimovich flowers.
From: Nicholas Fleming-Vázquez [view email]
[v1]
Thu, 20 Mar 2025 17:17:11 UTC (23 KB)
[v2]
Tue, 16 Jun 2026 13:28:57 UTC (22 KB)
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