An algebraic version of the central limit theorem

  • N. Giri
  • W. von Waldenfels


A non-commutative analogue of the central limit theorem and the weak law of large numbers has been derived, the analogues of integrable functions being non-commutative polynomials. Without the assumption of positivity higher central limit theorems hold which have no analogy in the classical probabilistic case. The treatment includes this classical case and the convergence to so-called “quasi-free states” in the quantum mechanics of bosons [3, 4].


Stochastic Process Quantum Mechanic Probability Theory Limit Theorem Mathematical Biology 
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    Robinson, D.W.: The Ground State of the Boson Gas. Comm. Math. Phys. 1, 159–174 (1964)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • N. Giri
    • 1
  • W. von Waldenfels
    • 2
  1. 1.Dept. des MathématiquesUniversité de MontréalMontréalCanada
  2. 2.Institut für Angewandte Mathematik der Universität HeidelbergHeidelbergBRD

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