Furkejuvvon:
| Váldodahkkit: | , |
|---|---|
| Materiálatiipa: | Preprint |
| Almmustuhtton: |
2020
|
| Fáttát: | |
| Liŋkkat: | https://arxiv.org/abs/2004.02679 |
| Fáddágilkorat: |
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Sisdoallologahallan:
- 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.