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.
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Bennies, J., Kersting, G. A Random Walk Approach to Galton–Watson Trees. Journal of Theoretical Probability 13, 777–803 (2000). https://doi.org/10.1023/A:1007862612753
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DOI: https://doi.org/10.1023/A:1007862612753