A tracial quantum central limit theorem
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- by Greg Kuperberg PDF
- Trans. Amer. Math. Soc. 357 (2005), 459-471 Request permission
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 Johanssonโs theorem on the limiting distribution of the shape of a random word in a fixed alphabet as its length goes to infinity.References
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Additional Information
- Greg Kuperberg
- Affiliation: Department of Mathematics, University of California Davis, Davis, California 95616
- Email: greg@math.ucdavis.edu
- Received by editor(s): May 22, 2003
- Published electronically: December 15, 2003
- Additional Notes: The author was supported by NSF grant DMS #0072342
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 459-471
- MSC (2000): Primary 46L53, 81S25; Secondary 60F05
- DOI: https://doi.org/10.1090/S0002-9947-03-03449-4
- MathSciNet review: 2095618