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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 33, Fasc. 2,
pages 255 - 264
 

THE PROBABILITY MEASURE CORRESPONDING TO 2-PLANE TREES

Wojciech Młotkowski
Karol A. Penson

Abstract: We study the probability measure μ 0 for which the moment sequence is (3n)-1- n n+1 . We prove that μ 0 is absolutely continuous, find the density function and prove that μ 0 is infinitely divisible with respect to the additive free convolution.

2000 AMS Mathematics Subject Classification: Primary: 44A60; Secondary: 46L54.

Keywords and phrases: Beta distribution, additive and multiplicative free convolution, Meijer G -function.

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