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.
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