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    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, 480, 2, 2003 DOI: 10.1016/j.jmaa.2019.06.065

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Type B Gaussian Statistics as Noncommutative Central Limits

Research output: Contribution to journalJournal articlepeer-review

Published
Article number123294
<mark>Journal publication date</mark>1/12/2019
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number2
Volume480
Number of pages13
Publication StatusPublished
Early online date27/06/19
<mark>Original language</mark>English

Abstract

We show that the noncommutative Central Limit Theorem of Speicher can be adapted to produce the Gaussian statistics associated to Coxeter groups of type B, in the sense of Bo˙zejko, Ejsmont, and Hasebe. Viewed through the lens of central limits, the passage from q-Gaussian statistics, associated with symmetric groups, to the Gaussian statistics associated with Coxeter groups of type B is precisely the passage from a sequence of independent elements that pairwise commute or anticommute, to a coupled pair of such sequences. The results pave the way for the transfer of known results from the bosonic/fermionic settings to such broader contexts.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, 480, 2, 2003 DOI: 10.1016/j.jmaa.2019.06.065