Conditioning Galton–Watson Trees on Large Maximal Outdegree

Xin He ()
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Xin He: Beijing Normal University

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 842-851

Abstract: Abstract We propose a new way to condition random trees, that is, conditioning random trees to have large maximal outdegree. Under this conditioning, we show that conditioned critical Galton–Watson trees converge locally to size-biased trees with a unique infinite spine. For the subcritical case, we obtain the local convergence to size-biased trees with a unique infinite node. We also study the tail of the maximal outdegree of subcritical Galton–Watson trees, which is essential for the proof of the local convergence.

Keywords: Random tree; Local limit; Kesten’s tree; Condensation tree; 60J80; 60B10 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-016-0664-x

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