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Pruning a Lévy continuum random tree

Abstract : 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 Lévy snake techniques. We then prove that the resulting sub-tree after pruning is still a Lévy 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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https://hal.archives-ouvertes.fr/hal-00270803
Contributor : Romain Abraham <>
Submitted on : Monday, July 12, 2010 - 11:49:35 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Thursday, October 14, 2010 - 3:28:48 PM

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  • HAL Id : hal-00270803, version 3
  • ARXIV : 0804.1027

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Romain Abraham, Jean-François Delmas, Guillaume Voisin. Pruning a Lévy continuum random tree. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2010, 15, pp.1429-1473. ⟨hal-00270803v3⟩

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