自由Poisson代数上的Poisson收敛
Poisson convergence on the free Poisson algebra
摘要：
基于Bourguin和Peccati的最新研究结果，给出了任意阶自由Poisson混沌的一个元素收敛于自由（中心）泊松分布的一个四阶矩型条件.我们还证明了严格大于1阶的自由Poisson混沌不包含任何非零的自由Poisson随机变量。我们还能够给出第一个自由泊松混沌的元素具有自由泊松分布的充分必要条件。最后，根据所考虑的自由泊松混沌的奇偶性，我们提供了一个一般的反例的天真普遍性的半圆维格纳混沌建立的Deya和Nourdin以及之间的转移原则的维格纳和自由泊松混沌。
英文摘要：
Based on recent findings by Bourguin and Peccati, we give a fourth moment type condition for an element of a free Poisson chaos of arbitrary order to converge to a free (centered) Poisson distribution. We also show that free Poisson chaos of order strictly greater than one do not contain any non-zero free Poisson random variables. We are also able to give a sufficient and necessary condition for an element of the first free Poisson chaos to have a free Poisson distribution. Finally, depending on the parity of the considered free Poisson chaos, we provide a general counterexample to the naive universality of the semicircular Wigner chaos established by Deya and Nourdin as well as a transfer principle between the Wigner and the free Poisson chaos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
