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2010 Pruning a Lévy Continuum Random Tree
Romain Abraham, Jean-François Delmas, Guillaume Voisin
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Electron. J. Probab. 15: 1429-1473 (2010). DOI: 10.1214/EJP.v15-802


Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated Lévy continuum random tree. This pruning procedure is defined by adding some marks on the tree, using L'evy snake techniques. We then prove that the resulting sub-tree after pruning is still a L'evy continuum random tree. This last result is proved using the exploration process that codes the CRT, a special Markov property and martingale problems for exploration processes. We finally give the joint law under the excursion measure of the lengths of the excursions of the initial exploration process and the pruned one.


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Romain Abraham. Jean-François Delmas. Guillaume Voisin. "Pruning a Lévy Continuum Random Tree." Electron. J. Probab. 15 1429 - 1473, 2010.


Accepted: 27 September 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1231.60073
MathSciNet: MR2727317
Digital Object Identifier: 10.1214/EJP.v15-802

Primary: 60J25
Secondary: 60G57 , 60J80

Keywords: Continuum random tree , Lévy snake , special Markov property


Vol.15 • 2010
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