Martingale Methods for Maximal Large Deviations and Young Towers

Fuente: arXiv
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Hauptverfasser: Alves, José F., Matias, João S., Melbourne, Ian
Format: Preprint
Veröffentlicht: 2026
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author Alves, José F.
Matias, João S.
Melbourne, Ian
author_facet Alves, José F.
Matias, João S.
Melbourne, Ian
contents We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain Young structures with matching recurrence tails for partially hyperbolic diffeomorphisms with mostly expanding central direction. In a second application, we prove maximal large deviation estimates for systems modelled by Young towers with subexponential contraction and expansion. Many examples of slowly mixing billiards are covered by this result.
format Preprint
id arxiv_https___arxiv_org_abs_2605_05968
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Martingale Methods for Maximal Large Deviations and Young Towers
Alves, José F.
Matias, João S.
Melbourne, Ian
Dynamical Systems
Probability
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain Young structures with matching recurrence tails for partially hyperbolic diffeomorphisms with mostly expanding central direction. In a second application, we prove maximal large deviation estimates for systems modelled by Young towers with subexponential contraction and expansion. Many examples of slowly mixing billiards are covered by this result.
title Martingale Methods for Maximal Large Deviations and Young Towers
topic Dynamical Systems
Probability
url https://arxiv.org/abs/2605.05968