Type B Gaussian Statistics as Noncommutative Central Limits

Blitvic, Natasha and Ejsmont, Wiktor (2019) Type B Gaussian Statistics as Noncommutative Central Limits. Journal of Mathematical Analysis and Applications, 480 (2). ISSN 0022-247X

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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.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Analysis and Applications
Additional Information:
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
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
135004
Deposited By:
Deposited On:
02 Jul 2019 11:40
Refereed?:
Yes
Published?:
Published
Last Modified:
29 Mar 2020 06:31