Probability Theory and Related Fields

, Volume 84, Issue 2, pp 141–159

A new example of ‘independence’ and ‘white noise’

  • Roland Speicher

DOI: 10.1007/BF01197843

Cite this article as:
Speicher, R. Probab. Th. Rel. Fields (1990) 84: 141. doi:10.1007/BF01197843


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 ofL2 (—).

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Roland Speicher
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergGermany

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