| Publication type: |
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Article in peer-reviewed journal |
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| Subject: |
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Mathematics/Probability
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| Title: |
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Pruning Galton-Watson Trees and Tree-valued Markov Processes |
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| Author(s): |
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Romain Abraham ( ) 1, Jean-François Delmas (,  ) 2, Hui He 1, 3 |
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| Laboratory: |
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| Abstract: |
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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. |
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| Fulltext language: |
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English |
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| Production date: |
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2010-07-02 |
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| Journal: |
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| Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques |
| Publisher |
Institute Henri Poincaré |
| ISSN |
0246-0203 |
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| Audience: |
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international |
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| Publication date: |
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2012 |
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| Volume: |
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48 |
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| Issue: |
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3 |
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| Page, identifiant, ...: |
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688-705 |
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| Keyword(s): |
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Branching process – Galton-Watson process – random tree – ascension process |
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| Classification: |
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05C05, 60J80, 60J27 |
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| ANR Project: |
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| Project Id |
ANR-08-BLAN-0190 |
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