The probability measure corresponding to 2-plane trees

preprint2013arXivOpen access

Abstract

We study the probability measure μ0μ_{0} for which the moment sequence is (3nn)1n+1\binom{3n}{n}\frac{1}{n+1}. We prove that μ0μ_{0} is absolutely continuous, find the density function and prove that μ0μ_{0} is infinitely divisible with respect to the additive free convolution.

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