EVENT DETAILS AND ABSTRACT

Title: Speed of random walks on groups and minimal growth of harmonic functions
Speaker: Tianyi Zheng
Speaker Info: University of California, San Diego
Brief Description:
Special Note: This seminar is joint with Algebra Seminar
Abstract:

We discuss a flexible construction of groups where the speed (rate of escape) of simple random walk can follow any sufficiently nice function between diffusive and linear. Minimal growth of non-constant harmonic functions on these groups are tightly related to the speed of the random walk. While in a variant of this construction, all harmonic functions of sub-exponential growth factor through a projection to a lamplighter. In particular we show that there exist groups on which all sub-linear harmonic functions are constant, while the speed of simple random walk can follow any prescribed super-diffusive function.