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Communications in Mathematical Physics

, Volume 137, Issue 3, pp 519–531 | Cite as

An example of a generalized Brownian motion

  • Marek Bożejko
  • Roland Speicher
Article

Abstract

We present an example of a generalized Brownian motion. It is given by creation and annihilation operators on a “twisted” Fock space ofL2(ℝ). These operators fulfill (for a fixed −1≦μ≦1) the relationsc(f)c*(g)−μc*(g)c(f)=〈f,g〉1 (f, gL2(ℝ)). We show that the distribution of these operators with respect to the vacuum expectation is a generalized Gaussian distribution, in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula. We also indicate that our Brownian motion is one component of ann-dimensional Brownian motion which is invariant under the quantum groupS ν U(n) of Woronowicz (withμ =v2).

Keywords

Neural Network Gaussian Distribution Statistical Physic Complex System Brownian Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Marek Bożejko
    • 1
  • Roland Speicher
    • 2
  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergFederal Republic of Germany

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