### The Width of Galton-Watson Trees Conditioned by the Size

*Michael Drmota, Bernhard Gittenberger*

#### 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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