Geodesic
The Width of Galton-Watson Trees Conditioned by the Size
Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2.

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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. 
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     title = {The {Width} of {Galton-Watson} {Trees} {Conditioned} by the {Size}},
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Drmota, Michael; Gittenberger, Bernhard. The Width of Galton-Watson Trees Conditioned by the Size. Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2. doi : 10.46298/dmtcs.323. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.323/

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