The Width of Galton-Watson Trees Conditioned by the Size

Michael Drmota (1) , Bernhard Gittenberger (1)

1 Institut für Diskrete Mathematik und Geometrie [Wien]

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.

Mots clés: branching processes; simply generated tree; generating functions; convergence of moments

Domaines: Mathématique discrète [cs.DM]

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