Type B Gaussian statistics as noncommutative central limits

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:480

Article

Blitvic, Natasha¹  Ejsmont, Wiktor² 

[1] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YW, England

[2] Univ Wroclaw, Math Inst, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

关键词: Central Limit Theorem;    Gaussians;    Coxeter groups;    Free probability;    Quantum probability;   

DOI  :  10.1016/j.jmaa.2019.06.065

来源: Elsevier

【 摘 要 】

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 Bozejko, 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free