论文标题
自由切线法
The Free Tangent Law
论文作者
论文摘要
Nevanlinna-Herglotz函数在自由概率中无限可划分的分布研究中起着基本作用。在本文中，我们研究了切线函数的作用，这是自由概率中基本的Herglotz-Nevanlinna函数和相关功能。具体来说，我们表明carlitz和Scoville的功能$$ \ frac {\ tan z} {1-x \ tan z} $$描述了自由交通剂和抗议机的限制分布，因此自由累积者由Euler Zigzag数字给出。
Nevanlinna-Herglotz functions play a fundamental role for the study of infinitely divisible distributions in free probability. In the present paper we study the role of the tangent function, which is a fundamental Herglotz-Nevanlinna function and related functions in free probability. To be specific, we show that the function $$ \frac{\tan z}{1-x\tan z} $$ of Carlitz and Scoville describes the limit distribution of sums of free commutators and anticommutators and thus the free cumulants are given by the Euler zigzag numbers.
