Abstract
Nevanlinna-Herglotz functions play a fundamental role for the study of infinitely divisible distributions in free probability [11]. In the present paper we study the role of the tangent function, which is a fundamental Herglotz-Nevanlinna function [28,23,54], and related functions in free probability. To be specific, we show that the function [Formula presented] of Carlitz and Scoville [17, (1.6)] describes the limit distribution of sums of free commutators and anticommutators and thus the free cumulants are given by the Euler zigzag numbers.
Original language | English |
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Article number | 102093 |
Journal | Advances in Applied Mathematics |
Volume | 121 |
DOIs | |
Publication status | Published - Oct 2020 |
Keywords
- Central limit theorem
- Cotangent sums
- Euler numbers
- Free infinite divisibility
- Tangent numbers
- Zigzag numbers
ASJC Scopus subject areas
- Applied Mathematics