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Probability and Dynamical Systems Seminar
Probability and Dynamical Systems Seminar
Trimmed Strong Laws and Distributional Limits for Exponentially Mixing Systems
Trimmed Strong Laws and Distributional Limits for Exponentially Mixing Systems
Organizers
Speaker
Time
Tuesday, June 16, 2026 3:15 PM - 4:15 PM
Venue
A3-3-301
Online
Zoom 482 240 1589
(BIMSA)
Abstract
The Birkhoff Ergodic Theorem guarantees pointwise convergence for integrable observables. However, for nonintegrable functions, no normalization can produce almost sure convergence to a nontrivial limit. We ask whether trimming, that is, removing a few extreme terms, can restore convergence, and if so, what limit distribution the trimmed sum follows. We answer these questions for observables with polynomial tails in exponentially mixing dynamical systems. We establish trimmed strong laws under light and intermediate trimming, together with the corresponding distributional limit theorems. This is joint work with Max Auer.
Speaker Intro
Sixu Liu received her Ph.D. degree from Peking University in 2019. She then worked as a postdoc at Tsinghua University before joining BIMSA as an assistant professor in 2022. Her main research interests include dynamical systems and ergodic theory, as well as statistical experimental design.