Oliver Sargent

Random walks on homogeneous spaces of non-lattice type

This is joint work with Uri Shapira. We attempt to generalise the spectacular
results of Y. Benoist and J.F. Quint to the homogeneous space consisting of
unimodular rank-2 discrete subgroups of R^3 . I will discuss the problem of
classifying stationary measures on this space. Under certain conditions on
the acting group we can show that there is a unique stationary probability
measure. We also have examples where (surprisingly) there is more than one
stationary probability measure. I will explain our results in both of these
situations.