Subadditive and Multiplicative Ergodic Theorems

Abstract

A result for subadditive ergodic cocycles is proved that provides more delicate information than Kingman's subadditive ergodic theorem. As an application we deduce a multiplicative ergodic theorem generalizing an earlier result of Karlsson-Ledrappier, showing that the growth of a random product of semi-contractions is always directed by some horofunction. We discuss applications of this result to ergodic cocycles of bounded linear operators, holomorphic maps and topical operators, as well as a random mean ergodic theorem.