Tianyi Zheng- Asymptotic Behaviors of Random Walks on Countable Groups

Explore the fascinating world of random walks on countable groups in this 43-minute lecture by Tianyi Zheng. Delve into Kesten's theorems, random walk entropy, and various themes surrounding this mathematical concept. Discover how random walks serve as powerful tools for studying groups acting on trees, volume growth, and graphs. Investigate more classes of intermediate growth groups and learn how random walks can be used to prove amenability. Examine groups with parameters and tackle random walk realization problems in this comprehensive exploration of asymptotic behaviors presented by the International Mathematical Union.

Syllabus

Introduction
Example
Kesten's theorems
Random walk entropy
A few themes
Random walks as tools
Use random walks to study groups acting on trees
Volume growth
Graphs
More classes of intermediate growth groups
Use random walks to prove amenability
Groups with parameters
Random walk realization problems