Discrete Mathematics & Theoretical Computer Science, Vol 6, No 2 (2004)

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DMTCS vol 6 no 2 (2004), pp. 387-400

Discrete Mathematics & Theoretical Computer Science


Volume 6 n° 2 (2004), pp. 387-400

author:Drmota, Michael and Gittenberger, Bernhard
title:The Width of Galton-Watson Trees Conditioned by the Size
keywords:branching processes, simply generated tree, generating functions, convergence of moments
abstract:It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance σ2 are asymptotically given by (σ√n)pmp where mp 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.

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reference: Drmota, Michael and Gittenberger, Bernhard (2004), The Width of Galton-Watson Trees Conditioned by the Size, Discrete Mathematics and Theoretical Computer Science 6, pp. 387-400
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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