Appears in collection : 2014 - T1 - Random walks and asymptopic geometry of groups.

According to a theorem of Furstenberg, a Zariski dense probability measure on a real semisimple Lie group admits a unique stationary probability measure on the flag variety. In this talk we will see that a Zariski dense probability measure on a p-adic semisimple Lie group admits finitely many stationary probability measures on the flag variety and we will classify these measures. This is a joint work with JF. Quint.