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Limit distributions for the number of leaves in a random forest

Part of: Markov processes Limit theorems Geometric probability and stochastic geometry Stochastic processes

Published online by Cambridge University Press:  01 July 2016

T. Mylläri
T. Mylläri*
Affiliation:
Åbo Akademi University and Petrozavodsk State University
*
∗ Postal address: Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland. Email address: tmioulli@abo.fi
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Abstract

Galton-Watson forests consisting of N roots (or trees) and n nonroot vertices are studied. The limit distributions of the number of leaves in such a forest are obtained. By a leaf we mean a vertex from which there are no arcs emanating.

Keywords

Conditioned Galton-Watson processlocal limit theoremnormal disributionoffspring distributionspanarray schemeMukhin's theorem

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F05: Central limit and other weak theorems 60D05: Geometric probability and stochastic geometry
Secondary: 60G50: Sums of independent random variables; random walks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 4 , December 2002 , pp. 904 - 922
Copyright
Copyright © Applied Probability Trust 2002 

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References

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