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Pruning Galton–Watson trees and tree-valued Markov processes

Romain Abraham, Jean-François Delmas, Hui He (2012)

Annales de l'I.H.P. Probabilités et statistiques

We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process { 𝒢 ( u ) } by pruning Galton–Watson trees and an analogous process { 𝒢 * ( u ) } by pruning a critical or subcritical Galton–Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process { 𝒢 ( u ) } run until its ascension time has a representation in terms of { 𝒢 * ( u ) } . A similar result was obtained by Aldous and...

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