  We consider the dynamics of an arbitrary quantum system coupled to a large
arbitrary and fully quantum mechanical environment through a random
interaction. We establish analytically and check numerically the typicality of
this dynamics, in other words the fact that the reduced density matrix of the
system has a self-averaging property. This phenomenon, which lies in a
generalized central limit theorem, justifies rigorously averaging procedures
over certain classes of random interactions and can explain the absence of
sensitivity to microscopic details of irreversible processes such as
thermalisation. It provides more generally a new ergodic principle for embedded
quantum systems.
