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A new example of ‘independence’ and ‘white noise’. (English) Zbl 0671.60109

We examine the notion of ‘free independence’ according to 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 \(L^ 2({\mathbb{R}})\).
Reviewer: R.Speicher

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
81P20 Stochastic mechanics (including stochastic electrodynamics)
60A99 Foundations of probability theory

Citations:

Zbl 0618.46048
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References:

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