Skip to Main content Skip to Navigation
Journal articles

Pruning Galton-Watson Trees and Tree-valued Markov Processes

Abstract : 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 $\{ {\cal G}(u)\}$ by pruning Galton-Watson trees and an analogous process $\{{\cal G}^*(u)\}$ 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 $\{{\cal G}(u)\}$ run until its ascension time has a representation in terms of $\{{\cal G}^*(u)\}$. A similar result was obtained by Aldous and Pitman (1998) in the special case of Poisson offspring distributions where they considered uniform pruning of Galton-Watson trees by adding marks on the edges of trees.
Complete list of metadatas

Cited literature [11 references]  Display  Hide  Download
Contributor : Romain Abraham <>
Submitted on : Monday, February 7, 2011 - 11:53:18 AM
Last modification on : Friday, May 4, 2018 - 1:17:28 AM
Document(s) archivé(s) le : Sunday, May 8, 2011 - 2:31:16 AM


Files produced by the author(s)




Romain Abraham, Jean-François Delmas, Hui He. Pruning Galton-Watson Trees and Tree-valued Markov Processes. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2012, 48 (3), pp.688-705. ⟨10.1214/11-AIHP423⟩. ⟨hal-00497035v2⟩



Record views


Files downloads