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Limit distribution of the quartet balance index for Aldous’s $(\beta \ge 0)$-model
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.ORCID iD: 0000-0002-5816-4345
2019 (English)In: Applicationes Mathematicae, ISSN 1233-7234, E-ISSN 1730-6280Article in journal (Refereed) Epub ahead of print
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Mathematics, Polish Academy of Science , 2019.
Keywords [en]
balance index, contraction method, phylogenetic tree, tree shape, weak convergence
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-159322DOI: 10.4064/am2385-6-2019OAI: oai:DiVA.org:liu-159322DiVA, id: diva2:1341000
Funder
Swedish Research Council, 2017-04951Knut and Alice Wallenberg FoundationAvailable from: 2019-08-07 Created: 2019-08-07 Last updated: 2019-09-05Bibliographically approved

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Bartoszek, Krzysztof

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