论文标题
限制定理和包装转换，无与伦比的概率理论
Limit Theorems and Wrapping Transforms in Bi-free Probability Theory
论文作者
论文摘要
在本文中，我们表征了与双腹部无与伦比的乘法卷积相对于双能分布的表征。同样，还获得了无限分布分布的无双重分配分布的无双重分布的三重态，而没有非平凡的态度因素。该三重态是独特的，并从无限分布的无限分布分布中产生同态。分析了与四个卷积，经典和无双重添加性卷积以及经典和无双性繁殖卷积相关的极限定理的相关性。该分析依赖于限制定理的收敛标准以及使用从平面到双道路的包装映射引起的推送措施的使用。与无与伦比的情况不同，经典的乘法Lévy三胞胎并不总是独特的。因此，提供了一些条件以确保独特性。
In this paper, we characterize idempotent distributions with respect to the bi-free multiplicative convolution on the bi-torus. Also, the bi-free analogous Levy triplet of an infinitely divisible distribution on the bi-torus without non-trivial idempotent factors is obtained. This triplet is unique and generates a homomorphism from the bi-free multiplicative semigroup of infinitely divisible distributions to the classical one. The relevances of the limit theorems associated with four convolutions, classical and bi-free additive convolutions and classical and bi-free multiplicative convolutions, are analyzed. The analysis relies on the convergence criteria for limit theorems and the use of push-forward measures induced by the wrapping map from the plane to the bi-torus. Different from the bi-free circumstance, the classical multiplicative Lévy triplet is not always unique. Due to this, some conditions are furnished to ensure uniqueness.
