Pruning a Lévy continuum random tree

Details Pruning a Lévy continuum random tree Pruning a Lévy continuum random tree

2008-04-07

arxiv.org/abs/0804.1027v3

Electronic Journal of Probability 15 (2010) 1429-1473

Mathematics

Probability

Scientific paper

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.

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