### Random walks on homogeneous spaces of non-lattice type

Ergodic Theory and Dynamical Systems Seminar

14th December 2017, 3:00 pm – 4:00 pm

Howard House, 4th Floor Seminar Room

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.

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