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 Electronic Journal of Probability > Vol. 15(2010) > Paper 46 open journal systems 


Pruning a Lévy continuum random tree

Romain Abraham, Université Orléans, MAPMO
Jean-François Delmas, Université Paris-Est, Cermics
Guillaume Voisin, Université Orléans, MAPMO


Abstract
Given a general critical or sub-critical branching mechanism, we define a pruning procedure of the associated L'evy 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.


Full text: PDF

Pages: 1429-1473

Published on: September 27, 2010
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Electronic Journal of Probability. ISSN: 1083-6489