R-对角和η-对角随机变量对

R-diagonal andη-diagonal Pairs of Random Variables

本文定义了双圆周(bi-circular)随机变量对(或称元素对),并证明其是R-对角的.我们给出了计算两个*-双自由的R-对角随机变量对的乘积对的分布的公式.对于由有限von Neumann代数里的算子组成的左、右作用随机变量对,我们用其随机变量的*-力矩(moments)刻画了R-对角性,定义了η-对角随机变量对,并用其分布的力矩性质刻画了分布的η-对角性.

We defining bi-circular element pairs of random variables,which provide examples of R-diagonal pairs of random variables.Formulae are given for calculating the distributions of the product pairs of two*-bi-free R-diagonal pairs.When focusing on pairs of left acting operators and right acting operators from finite von Neumann algebras in the standard form,we characterize R-diagonal pairs of random variables in terms of the *-moments of the random variables.Finally,we define η-diagonal pairs of random variables,and give a characterization of η-diagonal distributions in terms of the *-moments of the distribution.