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Local limits of Galton–Watson trees conditioned on the number of protected nodes
Published online by Cambridge University Press: 04 April 2017
Abstract
We consider a marking procedure of the vertices of a tree where each vertex is marked independently from the others with a probability that depends only on its out-degree. We prove that a critical Galton–Watson tree conditioned on having a large number of marked vertices converges in distribution to the associated size-biased tree. We then apply this result to give the limit in distribution of a critical Galton–Watson tree conditioned on having a large number of protected nodes.
MSC classification
Primary:
60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
60B10: Convergence of probability measures
Secondary:
05C05: Trees
- Type
- Research Papers
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- Copyright
- Copyright © Applied Probability Trust 2017
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