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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A tracial quantum central limit theorem


Author: Greg Kuperberg
Translated by:
Journal: Trans. Amer. Math. Soc. 357 (2005), 459-471
MSC (2000): Primary 46L53, 81S25; Secondary 60F05
Published electronically: December 15, 2003
MathSciNet review: 2095618
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be considered a generalization of Johansson's theorem on the limiting distribution of the shape of a random word in a fixed alphabet as its length goes to infinity.


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Additional Information

Greg Kuperberg
Affiliation: Department of Mathematics, University of California Davis, Davis, California 95616
Email: greg@math.ucdavis.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03449-4
PII: S 0002-9947(03)03449-4
Received by editor(s): May 22, 2003
Published electronically: December 15, 2003
Additional Notes: The author was supported by NSF grant DMS #0072342
Article copyright: © Copyright 2003 American Mathematical Society