Title: Random walk on homogeneous spaces

Abstract: Let G/\Gamma be a finite volume quotient of a Lie group by a discrete subgroup.
Let \mu be a probability measure on G.
Consider the random walk on G/\Gamma by which every point x goes to g.x where g ~ \mu.
New results classify the limit of distribution of the nth point in the random walk (as n -> infty) under certain assumptions on mu.
We will discuss the history of the problem and the ideas going into the proof.