Preprint, May 2026.
Jose Alvés, João Matias and Ian Melbourne
Abstract
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.