Abstract:
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 stationary measures on the
underlying step distributions on the group. The talk is based on joint
work with Behrang Forghani.