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.