A new example of `independence' and `white noise' (Q1119297)

We examine the notion of `free independence' according to \textit{D. Voiculescu} [see Lect. Notes Math. 1132, 556-588 (1985; Zbl 0618.46048)]. 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 analogous of the Wiener process and of the Poisson process as processes on the full Fock space of \(L^ 2({\mathbb{R}})\).