English

The probability measure corresponding to 2-plane trees

Probability 2013-12-12 v2 Combinatorics

Abstract

We study the probability measure μ0\mu_{0} for which the moment sequence is (3nn)1n+1\binom{3n}{n}\frac{1}{n+1}. We prove that μ0\mu_{0} is absolutely continuous, find the density function and prove that μ0\mu_{0} is infinitely divisible with respect to the additive free convolution.

Keywords

Cite

@article{arxiv.1304.6544,
  title  = {The probability measure corresponding to 2-plane trees},
  author = {Wojciech Mlotkowski and Karol A. Penson},
  journal= {arXiv preprint arXiv:1304.6544},
  year   = {2013}
}
R2 v1 2026-06-22T00:05:25.371Z