The free tangent law
Advances in Applied Mathematics, ISSN: 0196-8858, Vol: 121, Page: 102093
2020
- 7Citations
- 1Captures
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Article Description
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 tanz1−xtanz 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.
Bibliographic Details
http://www.sciencedirect.com/science/article/pii/S0196885820300968; http://dx.doi.org/10.1016/j.aam.2020.102093; http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=85089420524&origin=inward; https://linkinghub.elsevier.com/retrieve/pii/S0196885820300968; https://dx.doi.org/10.1016/j.aam.2020.102093
Elsevier BV
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