Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model

Volume 47 / 2020

Krzysztof Bartoszek 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


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.


  • Krzysztof BartoszekDepartment of Computer and Information Science
    Linköping University
    Linköping 581 83, Sweden
    ORCID: 0000-0002-5816-4345

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