# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 2 (2004), pp. 387-400

author: | Drmota, Michael and Gittenberger, Bernhard |
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title: | The Width of Galton-Watson Trees Conditioned by the Size |

keywords: | branching processes, simply generated tree, generating functions, convergence of moments |

abstract: | It is proved that the moments of the width of Galton-Watson trees of size n and with offspring variance σ are asymptotically
given by ^{2}(σ√n) where ^{p}m_{p}m 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.
_{p}If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Drmota, Michael and Gittenberger, Bernhard (2004),
The Width of Galton-Watson Trees Conditioned by the Size,
Discrete Mathematics and Theoretical Computer Science 6, pp. 387-400 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Mo Sep 13 15:40:03 CEST 2004 by gustedt