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Compound bi-free Poisson distributions

机译：复合双泊松分布

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摘要

In this paper, we study compound bi-free Poisson distributions for 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.
机译：在本文中，我们研究了两种随机变量家庭的复合双泊松分布。我们证明了复合双泊松分布的泊松极限定理。此外，对于双面自伴随随机变量的双面家庭自伴随随机变量的无限无限分割分布可以实现为双面自伴随随机变量的两面家庭的复合双泊松分布序列的极限。如果复合双泊松分布由正数和两个面对许多随机变量的分布有几乎肯定的随机矩阵模型，并且左随机变量与右随机变量通勤双面家庭，然后我们可以为复合双泊松分布构建一个随机的双矩阵模型。如果通过阳性数量和换向对随机变量的分布确定复合双泊松分布，我们可以构建具有创建和湮灭运营商的参赛作用者的渐近双矩阵模型，用于复合双泊泊榫分布。

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