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2011 A Note on the Probability of Cutting a Galton-Watson Tree
Luc Devroye
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Electron. J. Probab. 16: 2001-2019 (2011). DOI: 10.1214/EJP.v16-952

Abstract

The structure of Galton-Watson trees conditioned to be of a given size is well-understood. We provide yet another embedding theorem that permits us to obtain asymptotic probabilities of events that are determined by what happens near the root of these trees. As an example, we derive the probability that a Galton-Watson tree is cut when each node is independently removed with probability p, where by cutting a tree we mean that every path from root to leaf must have at least one removed node.

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Luc Devroye. "A Note on the Probability of Cutting a Galton-Watson Tree." Electron. J. Probab. 16 2001 - 2019, 2011. https://doi.org/10.1214/EJP.v16-952

Information

Accepted: 24 October 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1244.60087
MathSciNet: MR2851053
Digital Object Identifier: 10.1214/EJP.v16-952

Subjects:
Primary: 60J80
Secondary: 60G99, 60J85

JOURNAL ARTICLE
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Vol.16 • 2011
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