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math.DS2026
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…
math.DS2025
An analogue of Law of Iterated Logarithm for Heavy Tailed Random Variables
Dmitry Dolgopyat, Sixu Liu
We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite varianc…
math.DS2024
Generalized multiple Borel-Cantelli Lemma in dynamics and its applications
Sixu Liu
Multiple Borel-Cantelli Lemma is a criterion that characterizes the occurrence of multiple rare events on the same time scale. We generalize the multiple Borel-Cantelli Lemma in dy…