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On the asymptotic joint distribution of height and width in random trees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2008 (English)In: Studia scientiarum mathematicarum Hungarica (Print), ISSN 0081-6906, E-ISSN 1588-2896, Vol. 45, no 4, 451-467 p.Article in journal (Refereed) Published
Abstract [en]

It has been known for a long time that the height and width of a random labelled rooted tree, or of any other conditioned Galton-Watson tree, after suitable normalizations converge to the same limit distribution. Moreover, Chassaing, Marckert and Yor [7] have proved joint convergence of height and width. The resulting two-dimensional limit distribution has been studied by Donati-Martin [10]. we extend her results and give new formulas for joint moments. As an example, we calculate the covariance. We also show that the two-dimensional distribution is not symmetric, although the marginals are the same

Place, publisher, year, edition, pages
2008. Vol. 45, no 4, 451-467 p.
Keyword [en]
Conditioned Galton-Watson trees, random trees, height, width, Brownian excursion
National Category
URN: urn:nbn:se:uu:diva-106252DOI: 10.1556/SScMath.2007.1064ISI: 000260856800002OAI: oai:DiVA.org:uu-106252DiVA: diva2:224334
Available from: 2009-06-17 Created: 2009-06-17 Last updated: 2012-07-26Bibliographically approved

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Janson, Svante
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