Download PDF - A mixed quantum-classical central limit theoremAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

A mixed quantum-classical central limit theorem

Authors 1

Affiliations

  1. Institut Elie Cartan and LORIA, Université Henri Poincaré-Nancy 1, B.P. 239, F-54506 Vandœuvre-lès-Nancy, France

Abstract

A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex parameter is shown.

Bibliography

  1. [BKS96] M. Bożejko, B. Kümmerer and R. Speicher, q-Gaussian processes: Non-commutative and classical aspects, Commun. Math. Phys. 185 (1997), 129-154.
  2. [BS91] M. Bożejko and R. Speicher, An example of a generalized Brownian motion, Commun. Math. Phys. 137 (1991), 519-531.
  3. [Fra97a] U. Franz, Contribution à l'étude des processus stochastiques sur les groupes quantiques, Ph.D. Thesis, Université H. Poincaré-Nancy 1, 1997.
  4. [Fra97b] U. Franz, Classical versions of quantum Lévy processes, in preparation.
  5. [Sch91] M. Schürmann, Quantum q-white noise and a q-central limit theorem, Commun. Math. Phys. 140 (1991), 589-615.
  6. [Sch93] M. Schürmann, White Noise on Bialgebras, Berlin, Springer-Verlag, 1993, Lecture Notes in Mathematics, volume 1544.
  7. [Spe92] R. Speicher, A non-commutative central limit theorem, Math. Z. 209 (1992), 55-66.
Banach Center Publications
1998/43/1
Export to PBN, Opens in new tab
Pages:
183-189
Main language of publication
English
Published
1998
Exact and natural sciences