复合无Bi泊松分布
Compound Bi-free Poisson Distributions
摘要：
本文研究了{ \sl双面随机变量族}的复合双自由泊松分布。证明了复合双自由泊松分布的一个泊松极限定理。进一步地，双面自伴随机变量族的双自由无穷可分分布可以实现为双面自伴随机变量族的复合双自由泊松分布序列的极限.如果复合双自由泊松分布由一个正数和一个具有几乎几乎必然随机矩阵模型的两个面族的分布所确定，且两个面族中左随机变量与右随机变量可交换，则可以构造复合双自由泊松分布的随机双矩阵模型.如果复合双自由泊松分布由一个正数和一个可交换的随机变量对的分布所确定，我们可以构造一个复合双自由泊松分布的具有生成算子和湮灭算子的渐近双矩阵模型.
英文摘要：
In this paper, we study compound bi-free Poisson distributions for {\sl two-faced families of random variables}. We prove a Poisson limit theorem for compound bi-free Poisson distributions. Furthermore, a bi-free infinitely divisible distribution for a two-faced family of self-adjoint random variables can be realized as the limit of a sequence of compound bi-free Poisson distributions of two-faced families of self-adjoint random variables. If a compound bi-free Poisson distribution is determined by a positive number and the distribution of a two faced family of finitely many random variables, which has an almost sure random matrix model, and the left random variables commute with the right random variables in the two-faced family, then we can construct a random bi-matrix model for the compound bi-free Poisson distribution. If a compound bi-free Poisson distribution is determined by a positive number and the distribution of a commutative pair of random variables, we can construct an asymptotic bi-matrix model with entries of creation and annihilation operators for the compound bi-free Poisson distribution.
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