题   目: Trimmed strong laws and distributional limits for exponentially mixing systems

报告人: 刘思序 (北京雁栖湖应用数学研究院)

时间地点: 数学学院新楼 308，5月12日（周二）16:00-17:00

摘   要：The Birkhoff Ergodic Theorem establishes pointwise convergence for integrable observables, but for non-integrable functions, no normalization yields almost sure convergence. We consider trimmed ergodic sums, where the largest observations are removed, for observables with polynomial tails in exponentially mixing dynamical systems. Such observables are characterized by a positive parameter that governs the tail decay rate. We establish trimmed strong laws of large numbers when this parameter is at least 1, extending classical results from the i.i.d. setting. In addition, we prove distributional limit theorems for both lightly and intermediately trimmed sums when the parameter exceeds 1/2, showing convergence to a non-standard limit law and a normal distribution, respectively. This is joint work with Max Auer.