In the absence of measures fully invariant with respect to a group action, this role can be to a certain extent played by the measures “invariant on average”, with respect to a certain fixed distribution on the group. These measures are called stationary, and they naturally arise as harmonic measures of random walks. I will provide several partial answers to the general question about the dependence of harmonic measures on the underlying step distributions on the group and discuss counterexamples related to the Minkowski and Denjoy measure classes on the boundary of the classical modular group.
The talk is based on joint work with Behrang Forghani.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
