Examples of measures with trivial left and non-trivial right random walk tail boundary

Abstract

In early 80's Vadim Kaimanovich presented a construction of a non-degenerate measure, on the standard lamplighter group, that has a trivial left and non-trivial right random walk tail boundary. We show that examples of such kind are possible precisely for amenable groups that have non-trivial factors with infinite conjugacy classes property.

arXiv comment11 pages, improved presentation