The Width of Galton-Watson Trees Conditioned by the Size
Authors: Michael Drmota 1; Bernhard Gittenberger 1
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Michael Drmota;Bernhard Gittenberger
1 Institut für Diskrete Mathematik und Geometrie [Wien]
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.
Automatic Expansion of Generating Functions; Funder: Austrian Science Fund (FWF); Code: P 16053
3 Documents citing this article
Source : OpenCitations
Addario-Berry, Louigi; Devroye, Luc; Janson, Svante, 2013, Sub-Gaussian Tail Bounds For The Width And Height Of Conditioned GaltonâWatson Trees, The Annals Of Probability, 41, 2, 10.1214/12-aop758.