A new example of 'independence' and 'white noise'

Abstract

We examine the notion of 'free independence' according to Voiculescu. This form of independence is used for defining 'free white noise' or 'process with stationary and freely independent increments'. We prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of 'admissible' partitions. We realize the free analogues of the Wiener process and of the Poisson process as processes on the full Fock space of L2 (-). © 1990 Springer-Verlag.