Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912284195946496 |
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| author | Fleming-Vázquez, Nicholas |
| author_facet | Fleming-Vázquez, Nicholas |
| contents | 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 $p<\infty$. Additionally, this is the first result on rates that covers certain invertible, slowly mixing maps, such as Bunimovich flowers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps Fleming-Vázquez, Nicholas Dynamical Systems 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 $p<\infty$. Additionally, this is the first result on rates that covers certain invertible, slowly mixing maps, such as Bunimovich flowers. |
| title | Rates of convergence in the multivariate weak invariance principle for nonuniformly hyperbolic maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2503.16358 |