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The Width of Galton-Watson Trees Conditioned by the Size

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.
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Michael Drmota, Bernhard Gittenberger. The Width of Galton-Watson Trees Conditioned by the Size. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2004, Vol. 6 no. 2 (2), pp.387-400. ⟨10.46298/dmtcs.323⟩. ⟨hal-00959015⟩

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