Some probabilistic trees with algebraic roots

2015/01/06 by Bernardi, Olivier, Morales, Alejandro H. · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.01135

Abstract

In this article we consider several probabilistic processes defining random grapha. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each of the probabilistic processes, we prove that the probability for the random graph to be a tree has an extremely simple expression, which is independent of most parameters of the problem. This raises many open questions.

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• Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements

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