LA Probability Forum

The study of stationary actions of groups and connections to random walks was initiated by Furstenberg, and later plays a role in the development of rigidity theory. The Furstenberg entropy is a fundamental invariant defined for a stationary system. In this talk we will discuss some aspect of the question: given a group, what is the range of the Furstenberg entropy of ergodic stationary actions of it? For the linear group SL(d,R) and its lattices, constraints on this spectrum are closely related to structure theorems due to Nevo and Zimmer; and entropy values can be realized based on random walks on random stationary graphs