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): 123294. 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.