Moments and $q$-commutators of noncommutative random vectors
Krzysztof Dro\.zd\.zewicz, Wojciech Matysiak
TL;DR
This paper introduces a method to compute mixed moments of noncommutative random vectors using first order moments and specific $q$-commutators, exemplified by $q$-Gaussian vectors.
Contribution
It presents a novel approach for calculating moments of noncommutative vectors based on $q$-commutators, enhancing understanding of their structure.
Findings
Method effectively computes mixed moments from first order moments and $q$-commutators.
Characterization of $q$-Gaussian vectors using the proposed method.
Provides a new tool for analyzing noncommutative random vectors.
Abstract
A method for computing the mixed moments of (not necessarily commutative) random vectors from the first order moments, the -commutators between the annihilation and creation operators, and the -commutators between the annihilation and preservation operators, is presented. The method is illustrated by a relevant characterization of -Gaussian vectors.
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