Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model
Volume 47 / 2020
Applicationes Mathematicae 47 (2020), 29-44
MSC: Primary 05C80, 60F05; Secondary 60J85, 62P10, 92B10, 92D15.
DOI: 10.4064/am2385-6-2019
Published online: 29 July 2019
Abstract
This paper builds on T. Martínez-Coronado, A. Mir, F. Rosselló and G. Valiente’s 2018 work, introducing a new balance index for trees. We show that this balance index, in the case of Aldous’s $(\beta \ge 0)$-model, converges weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.
