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Abstract: Given a general critical or sub-critical branching mechanism, we define apruning procedure of the associated L\-evy continuum random tree. This pruningprocedure is defined by adding some marks on the tree, using L\-evy snaketechniques. We then prove that the resulting sub-tree after pruning is still aL\-evy continuum random tree. This last result is proved using the explorationprocess that codes the CRT, a special Markov property and martingale problemsfor exploration processes. We finally give the joint law under the excursionmeasure of the lengths of the excursions of the initial exploration process andthe pruned one.



Author: Romain Abraham MAPMO, Jean-Francois Delmas CERMICS, Guillaume Voisin MAPMO

Source: https://arxiv.org/







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