Abstract
We recall a few elementary properties of supercritical Galton–Watson trees, and introduce the notion of size-biased trees. As an application, we give in Sect. 2.3 the beautiful conceptual proof by Lyons et al. (Ann Probab 23:1125–1138, 1995) of the Kesten–Stigum theorem for the branching process. The goal of this brief chapter is to give an avant-goût of the spinal decomposition theorem, in the simple setting of the Galton–Watson tree. If you are already familiar with any form of the spinal decomposition theorem, this chapter can be skipped.
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Shi, Z. (2015). Galton–Watson Trees. In: Branching Random Walks. Lecture Notes in Mathematics(), vol 2151. Springer, Cham. https://doi.org/10.1007/978-3-319-25372-5_2
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DOI: https://doi.org/10.1007/978-3-319-25372-5_2
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