A Random Walk Approach to Galton–Watson Trees

Jürgen Bennies and Götz Kersting
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Jürgen Bennies: University of Frankfurt
Götz Kersting: University of Frankfurt

Journal of Theoretical Probability, 2000, vol. 13, issue 3, 777-803

Abstract: Abstract There are several constructions connecting random walks to branching trees. Here we discuss an approach linking Galton–Watson trees with arbitrary offspring distribution to random walk excursions resp. bridges. In special situations this leads to a connection to three basic statistics from statistical mechanics. Other applications include the description of random subtrees and the contour process of a Galton–Watson tree.

Keywords: branching processes; Galton–Watson trees; random walk excursions; random walk bridges; functional limit theorem (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1023/A:1007862612753

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