a countable discrete group is said to be choquet-deny if it has a trivial poisson boundary for every non-degenerate probability measure on the group. in other words, a countable discrete group is choquet-deny if non-degenerate random walks on the group have trivial behavior at infinity. for example, all abelian groups are choquet-deny. it has been long known that all choquet-deny groups are amenable. i will present a recent result classifying countable discrete choquet-deny groups: a countable discrete group is choquet-deny if and only if none of its quotients have the infinite conjugacy class property. as a corollary, a finitely generated group is choquet-deny if and only if it is virtually nilpotent. this is a joint work with joshua frisch, yair hartman, and omer tamuz.