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Ladder variables, internal structure of Galton–Watson trees and finite branching random walks
Published online by Cambridge University Press: 14 July 2016
Abstract
In this paper, we consider Galton–Watson trees conditioned by size. We show that the number of k-ancestors (ancestors that have k children) of a node u is (almost) proportional to its depth. The k, j-ancestors are also studied. The methods rely on the study of ladder variables on an associated random walk. We also give an application to finite branching random walks.
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- Copyright © Applied Probability Trust 2003
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