1Institut für Diskrete Mathematik und Geometrie [Wien] (Forschungsgruppe Differentialgeometrie und Geometrische Strukturen Technische Universität Wien Wiedner Hauptstraße 8-10/104 A-1040 Wien, Austria - Autriche)
Abstract : It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance σ ^2 are asymptotically given by (σ √n)^pm_p where m_p are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a tightness estimate. The method is quite general and we state some further applications.
https://hal.inria.fr/hal-00959015
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s
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Soumis le : jeudi 13 mars 2014 - 17:06:19
Dernière modification le : mercredi 29 novembre 2017 - 10:26:21
Document(s) archivé(s) le : vendredi 13 juin 2014 - 12:12:32
Michael Drmota, Bernhard Gittenberger. The Width of Galton-Watson Trees Conditioned by the Size. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2004, 6 (2), pp.387-400. 〈hal-00959015〉
