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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
DOI: https://doi.org/10.1090/S0002-9939-2011-11015-3
Published electronically: May 24, 2011
MathSciNet review: 2813403
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. Alexeev, N., Götze, F., Tikhomirov, A.: Asymptotic distribution of singular values of powers of random matrices, Lithuanian Math. J. 50, no. 2 (2010), 121-132.
  • 2. Andrews, G. E., Askey, R., Roy, R.: Special Functions, Cambridge University Press (1999). MR 1688958 (2000g:33001)
  • 3. Banica, T., Belinschi, S., Capitaine, M., Collins, B.: Free Bessel laws, Canad. J. Math. 63 (2011), 3-37.
  • 4. Collins, B., Nechita, I., Życzkowski, K.: Random graph states, maximal flow and Fuss-Catalan distributions, J. Phys. A: Math. Theor. 43 (2010), 275-303. MR 2658283
  • 5. Liu, D.-Z., Wang, Z.-D., Yan, K.-H.: Density of eigenvalues and its perturbation invariance in unitary ensembles of random matrices, Journal of Approximation Theory 162, no. 9 (2010), 1588-1606. MR 2718887
  • 6. Młtkowski, W.: Fuss-Catalan numbers in noncommutative probability, Documenta Mathematica 15 (2010), 939-955.
  • 7. Nica, A., Speicher, R.: Lectures on the Combinatorics of Free Probability, Cambridge University Press (2006). MR 2266879 (2008k:46198)
  • 8. Penson, K. A., Solomon, A. I.: Coherent states from combinatorial sequences, arXiv:quant-ph/0111151v1
  • 9. Wigner, E. P.: Characteristic vectors of bordered matrices with infinite dimensions, Ann. of Math. (2) 62 (1955), 548-564. MR 0077805 (17:1097c)

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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: https://doi.org/10.1090/S0002-9939-2011-11015-3
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

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