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Almost sure convergence of vertex degree densities in the vertex splitting model
Univ Iceland, Inst Sci, Div Math, Dunhaga 3, IS-107 Reykjavik, Iceland..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Communications in Statistics. Stochastic Models, ISSN 1532-6349, E-ISSN 1532-4214, Vol. 32, no 4, 575-592 p.Article in journal (Refereed) Published
Abstract [en]

We study the limiting degree distribution of the vertex splitting model introduced in Ref.([3]). This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a vertex into two, and then inserting an edge between the two new vertices. Under some assumptions on the parameters, related to the growth of the maximal degree of the tree, we prove that the vertex degree densities converge almost surely to constants which satisfy a system of equations. Using this, we are also able to strengthen and prove some previously non-rigorous results mentioned in the literature.

Place, publisher, year, edition, pages
2016. Vol. 32, no 4, 575-592 p.
Keyword [en]
Almost sure convergence, degree densities, random trees, vertex splitting, 05C80, 05C05
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-303159DOI: 10.1080/15326349.2016.1182029ISI: 000380246200003OAI: oai:DiVA.org:uu-303159DiVA: diva2:970984
Available from: 2016-09-15 Created: 2016-09-15 Last updated: 2017-02-21Bibliographically approved

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