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

Mathematics > Dynamical Systems [Submitted on 20 Mar 2025 (v1), last revised 16 Jun 2026 (this version, v2)] Title:Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps View PDF HTML (experimental)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. Submission history 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) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.