Partitions with independent iterates in random dynamical systems

Abstract

AbstractKrengel characterized weakly mixing actions (X,T) as those measure-preserving actions having a dense set of partitions of X with infinitely many jointly independent images under iterates of T. Using the tools developed in later papers—one by del Junco, Reinhold and Weiss, another by del Junco and Begun—we prove analogues of these results for weakly mixing random dynamical systems (in other words, relatively weakly mixing systems).