Random walks and contracting elements III: Outer space and outer automorphism group

Continuing from the author’s previous article ‘Random walks and contracting elements I’, we study random walks on (possibly asymmetric) metric spaces using the bounded geodesic image property (BGIP) of certain isometries. As an application, we show that a generic outer automorphism of the free group of rank at least 3 has different forward and backward expansion factors. This answers a question of Handel and Mosher.