Michael Drmota ; Bernhard Gittenberger - The Width of Galton-Watson Trees Conditioned by the Size

dmtcs:323 - Discrete Mathematics & Theoretical Computer Science, January 1, 2004, Vol. 6 no. 2 - https://doi.org/10.46298/dmtcs.323
The Width of Galton-Watson Trees Conditioned by the SizeArticle

Authors: Michael Drmota 1; Bernhard Gittenberger ORCID1

  • 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.


Volume: Vol. 6 no. 2
Published on: January 1, 2004
Imported on: March 26, 2015
Keywords: branching processes,simply generated tree,generating functions,convergence of moments,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Automatic Expansion of Generating Functions; Funder: Austrian Science Fund (FWF); Code: P 16053

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