Moments and $q$-commutators of noncommutative random vectors
  A method for computing the mixed moments of (not necessarily commutative) random vectors from the first order moments, the $q$-commutators between the annihilation and creation operators, and the $q$-commutators between the annihilation and preservation operators, is presented. The method is illustrated by a relevant characterization of $q$-Gaussian vectors. 
Krzysztof Dro\.zd\.zewicz and Wojciech Matysiak
math.PR