Type B Gaussian Statistics as Noncommutative Central Limits
Probability
2019-07-24 v2 Operator Algebras
Quantum Algebra
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. Specifically, we show how type B Gaussian statistics naturally arise in systems of 'mixed spins', providing a new application of Speicher's argument and paving the way for the transfer of known results from the bosonic/fermionic settings to such broader contexts.
Keywords
Cite
@article{arxiv.1807.03580,
title = {Type B Gaussian Statistics as Noncommutative Central Limits},
author = {Natasha Blitvić and Wiktor Ejsmont},
journal= {arXiv preprint arXiv:1807.03580},
year = {2019}
}
Comments
Final version. Typo fixes and a minor correction to the normalization factor