6 papers
Quenched limit theorems via mixing of all orders for random dynamical systems
Max Auer
We adapt the notion of mixing of all orders to random dynamical systems and use it to establish quenched limit theorems. Assuming quenched exponential mixing of all orders, we prov…
Trimmed strong laws and distributional limits for exponentially mixing systems
Max Auer, Sixu Liu
The Birkhoff Ergodic Theorem establishes pointwise convergence for integrable observables, but for , no normalization yields almost sure convergence. This paper invest…
Trimmed ergodic sums for non-integrable functions with power singularities over irrational rotations
Max Auer, Tanja I. Schindler
Studying Birkhoff sums of non-integrable functions involves the challenge of large observations depending on the sampled orbit, which prevents pointwise limit theorems. To address…
Weak mixing and sparse equidistribution
Max Auer
The celebrated Birkhoff Ergodic Theorem asserts that, for an ergodic map, orbits of almost every point equidistributes when sampled at integer times. This result was generalized by…
Local limit theorems for hitting times and return times of small sets
Max Auer, Roland Zweimüller
We establish abstract local limit theorems for hitting times and return-times of suitable sequences (A_{l}) of asymptotically rare events in ergodic probability preserving dynamica…
Poisson Limit Theorems for Systems with Product Structure
Max Auer
We obtain a Poisson Limit for return times to small sets for product systems. Only one factor is required to be hyperbolic while the second factor is only required to satisfy polyn…