The Width of Galton-Watson Trees Conditioned by the SizeReport as inadecuate




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1 Institut für Diskrete Mathematik und Geometrie Wien

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.

Keywords : branching processes simply generated tree generating functions convergence of moments





Author: Michael Drmota - Bernhard Gittenberger -

Source: https://hal.archives-ouvertes.fr/



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