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Asymptotic Normality of Fringe Subtrees and Additive Functionals in Conditioned Galton-Watson Trees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 48, no 1, 57-101 p.Article in journal (Refereed) PublishedText
Abstract [en]

We consider conditioned Galton-Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. Another example is the number of protected nodes. The offspring distribution defining the random tree is assumed to have expectation 1 and finite variance; no further moment condition is assumed.

Place, publisher, year, edition, pages
2016. Vol. 48, no 1, 57-101 p.
Keyword [en]
fringe subtrees, conditioned Galton-Watson trees, additive functionals, toll functions
National Category
URN: urn:nbn:se:uu:diva-275857DOI: 10.1002/rsa.20568ISI: 000367622800004OAI: oai:DiVA.org:uu-275857DiVA: diva2:903612
Knut and Alice Wallenberg Foundation
Available from: 2016-02-16 Created: 2016-02-08 Last updated: 2016-02-16Bibliographically approved

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Janson, Svante
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