A mixed quantum-classical central limit theorem

U. Franz

Banach Center Publications (1998)

  • Volume: 43, Issue: 1, page 183-189
  • ISSN: 0137-6934

Abstract

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

How to cite

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Franz, U.. "A mixed quantum-classical central limit theorem." Banach Center Publications 43.1 (1998): 183-189. <http://eudml.org/doc/208837>.

@article{Franz1998,
abstract = {A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex parameter is shown.},
author = {Franz, U.},
journal = {Banach Center Publications},
keywords = {central limit theorem; Hopf algebra; bialgebra; -Brownian motion},
language = {eng},
number = {1},
pages = {183-189},
title = {A mixed quantum-classical central limit theorem},
url = {http://eudml.org/doc/208837},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Franz, U.
TI - A mixed quantum-classical central limit theorem
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 183
EP - 189
AB - A randomized q-central or q-commutative limit theorem on a family of bialgebras with one complex parameter is shown.
LA - eng
KW - central limit theorem; Hopf algebra; bialgebra; -Brownian motion
UR - http://eudml.org/doc/208837
ER -

References

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  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. Zbl0722.60033
  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. Zbl0734.60048
  6. [Sch93] M. Schürmann, White Noise on Bialgebras, Berlin, Springer-Verlag, 1993, Lecture Notes in Mathematics, volume 1544. Zbl0773.60100
  7. [Spe92] R. Speicher, A non-commutative central limit theorem, Math. Z. 209 (1992), 55-66. Zbl0724.60023

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