Speed of random walks on finitely generated groups
Speed of random walks on finitely generated groups

Tianyi Zheng , UCSD
Fine Hall 214
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. When the speed of the \murandom walk is sublinear, all bounded \muharmonic functions are constant. We investigate the minimal growth of nonconstant harmonic functions on these groups and show it is tightly related to the speed of the random walk. Based on joint works with Jeremie Brieussel, Gidi Amir and Gady Kozma.