Type B Gaussian Statistics as Noncommutative Central Limits

TL;DR

This paper extends Speicher's noncommutative central limit theorem to generate Gaussian statistics linked to Coxeter groups of type B, using systems of 'mixed spins' to connect known bosonic and fermionic results.

Contribution

It adapts Speicher's theorem to type B Gaussian statistics, introducing a new application involving mixed spin systems.

Findings

Type B Gaussian statistics arise naturally in mixed spin systems

The approach bridges bosonic and fermionic statistical frameworks

New methods for analyzing noncommutative probability models

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.