Central limit theorem associated to Gaussian operators of type B

TL;DR

This paper establishes a central limit theorem for Gaussian operators of type B using colored pair partitions and introduces noncommutative random matrix models for deformed Gaussian variables.

Contribution

It formulates a CLT for type B Gaussian operators and presents new noncommutative random matrix models for (,)-deformed Gaussian variables.

Findings

Established CLT for Gaussian operators of type B.

Introduced noncommutative random matrix models for deformed Gaussian variables.

Connected combinatorial structures with noncommutative probability.

Abstract

In this article we formulate the CLT associated to Gaussian operators of type B -- see \cite{BEH15}, where important role is played by colored pair partitions. Then we present a certain family of noncommutative random matrix models for the $(\alpha,q)$--deformed Gaussian random variables