A random walk approach to Galton-Watson trees
type: Item
instance of: scholarly article
title: A random walk approach to Galton-Watson trees
zbMATH Open document ID: 0977.60083
DOI: 10.1023/A:1007862612753
author: Jürgen Bennies
author: Götz Kersting
published in: Journal of Theoretical Probability
publication date: 2002-01-04T00:00:00Z
review text: An approach is discussed linking Galton-Watson trees with arbitrary offspring distributions to random walk excursions and bridges [this idea was used independently by \textit{J.-F. Le Gall} and \textit{Y. Le Jan}, Ann. Probab. 26, No. 1, 213-252 (1998; Zbl 0948.60071)]. Applying this approach the authors investigate Galton-Watson trees with binary, Poisson or geometric offspring distribution and reveal some connections to the Dirac, Bose-Einstein and Maxwell-Boltzmann statistics. They also analyze the structure of the subtree of all descendants of a randomly chosen individual of a tree conditioned to have fixed size \(n\), study the lines of ancestors and ladder points of a related random walk and use the established facts to construct Galton-Watson trees conditioned to survive a given number of generations.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 1552709
zbMATH Keywords: branching processes
zbMATH Keywords: Galton-Watson trees
zbMATH Keywords: random walk excursions
zbMATH Keywords: functional limit theorems
zbMATH Keywords: random walk bridges
reviewed by: Vladimir Vatutin
MaRDI profile type: Publication
full work available at URL: a:1007862612753
OpenAlex ID: W1506498195
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description: scientific article; zbMATH DE number 1552709