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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On explicit probability densities associated with Fuss-Catalan numbers


Authors: Dang-Zheng Liu, Chunwei Song and Zheng-Dong Wang
Journal: Proc. Amer. Math. Soc. 139 (2011), 3735-3738
MSC (2010): Primary 60B20, 46L54; Secondary 05A99
Published electronically: May 24, 2011
MathSciNet review: 2813403
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Abstract: In this paper we give explicitly a family of probability densities, the moments of which are Fuss-Catalan numbers. The densities appear naturally in random matrices, free probability and other contexts.


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Additional Information

Dang-Zheng Liu
Affiliation: School of Mathematical Sciences, LMAM, Peking University, Beijing, 100871, People’s Republic of China
Address at time of publication: Instituto Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
Email: dzliu@inst-mat.utalca.cl

Chunwei Song
Affiliation: School of Mathematical Sciences, LMAM, Peking University, Beijing, 100871, People’s Republic of China
Email: csong@math.pku.edu.cn

Zheng-Dong Wang
Affiliation: School of Mathematical Sciences, LMAM, Peking University, Beijing, 100871, People’s Republic of China
Email: zdwang@pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11015-3
PII: S 0002-9939(2011)11015-3
Keywords: Fuss-Catalan numbers, moments, free Bessel laws
Received by editor(s): August 4, 2010
Published electronically: May 24, 2011
Communicated by: Jim Haglund
Article copyright: © Copyright 2011 American Mathematical Society