The probability measure corresponding to 2-plane trees

• Autorzy: Młotkowski W. , Penson K. A.
• Języki publikacji: EN

Abstrakty

EN

We study the probability measure μ₀ for which the moment sequence is (3n/n) 1/n+1 . We prove that μ₀ is absolutely continuous, find the density function and prove that μ₀ is infinitely divisible with respect to the additive free convolution.

Słowa kluczowe

EN

beta distribution; additive free convolution; multiplicative free convolution; Meijer G-function

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 255--264
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Młotkowski W.

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Penson K. A.

• Laboratoire de Physique Théorique, de la Matière Condensée (LPTMC), Université Pierre et Marie Curie, CNRS UMR 7600, Tour 13 – 5ième ét., Boîte Courrier 121, 4 place Jussieu, F 75252 Paris Cedex 05, France

Bibliografia

• [1] N. Balakrishnan and V. B. Nevzorov, A Primer on Statistical Distributions, Wiley-Interscience, Hoboken, N. J., 2003.
• [2] R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics. A Foundation for Computer Science, Addison-Wesley, New York 1994.
• [3] N. S. S. Gu and H. Prodinger, Bijections for 2-plane trees and ternary trees, European J. Combin. 30 (2009), pp. 969-985.
• [4] N. S. S. Gu, H. Prodinger, and S. Wagner, Bijection for a class of labeled plane trees, European J. Combin. 31 (2010), pp. 720-732.
• [5] W. Młotkowski, Fuss-Catalan numbers in noncommutative probability, Doc. Math. 15 (2010), pp. 939-955.
• [6] W. Młotkowski, K. A. Penson, and K. Życzkowski, Densities of the Raney distributions, arXiv:1211.7259, Doc. Math., 2013 (in press).
• [7] A. Nica and R. Speicher, Lectures on the Combinatorics of Free Probability, Cambridge University Press, 2006.
• [8] K. A. Penson and K. Życzkowski, Product of Ginibre matrices: Fuss-Catalan and Raney distributions, Phys. Rev. E 83 (2011) 061118, 9 pp.
• [9] A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 3: More Special Functions, Gordon and Breach, Amsterdam 1998.
• [10] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences (2013), published electronically at: http://oeis.org/.
• [11] I. N. Sneddon, The Use of Integral Transforms, Tata McGraw-Hill Publishing Company, 1974.
• [12] D. V. Voiculescu, K. J. Dykema, and A. Nica, Free Random Variables, CRM Monogr. Ser., Amer. Math. Soc., 1992.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).