走向现代数学学术报告 - 蒋云平教授（No. 645）

报告题目：Decay Rate of Correlations in Dynamical Systems

报告人：蒋云平 教授（纽约市立大学）

时间：2023年7月21日 15:30

地点：学术报告厅（工西416）

摘要：The decay rate of correlations is an essential problem in studying dynamical systems. In this talk, I will connect the decay rate of correlations by looking at a transfer operator's spectrum gap. The spectrum gap implies the exponential day of correlations for locally expanding dynamical systems with Holder potentials. However, there is no spectrum gap for weakly expanding dynamical systems with Dini potentials; therefore, we cannot have exponential decay for correlations. But in my current research with Yuan-Ling Ye, we found an optimal quasi-gap for weakly expanding dynamical systems with Dini potentials. This optimal quasi-gap implies a decay rate for correlations. For some modulus of continuity, we can use our decay rate estimation to verify the central limit theorem for weakly expanding dynamical systems with Dini potentials.  

报告人简介：蒋云平，纽约市立大学讲座教授，著名动力系统专家。大学本科和研究生毕业于北京大学，师从廖山涛教授，博士毕业于美国纽约市立大学研究生院，师从D. Sullivan教授（Abel奖得主），中科院百人计划入选者，曾任美国数学学会Transactions和Memoirs的编辑，美国国家科学基金会数学分析组主任。