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Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Annals of Probability, ISSN 0091-1798, Vol. 41, no 2, 1072-1087 p.Article in journal (Refereed) Published
Abstract [en]

We study the height and width of a Galton-Watson tree with offspring distribution xi satisfying E xi = 1, 0 < Var xi < infinity, conditioned on having exactly n nodes. Under this conditioning, we derive sub-Gaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of nodes at level k, for 1 <= k <= n.

Place, publisher, year, edition, pages
2013. Vol. 41, no 2, 1072-1087 p.
Keyword [en]
Random trees, Galton-Watson trees, simply generated trees, width, height
National Category
Natural Sciences
URN: urn:nbn:se:uu:diva-199732DOI: 10.1214/12-AOP758ISI: 000317157300019OAI: oai:DiVA.org:uu-199732DiVA: diva2:621029
Available from: 2013-05-13 Created: 2013-05-13 Last updated: 2013-05-13Bibliographically approved

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Janson, Svante
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