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Article Dans Une Revue Stochastic Processes and their Applications Année : 2013

The forest associated with the record process on a Lévy tree

Résumé

We perform a pruning procedure on a Lévy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the Lévy tree). We prove that the tree constructed by regrafting is distributed as the original Lévy tree, generalizing a result where only Aldous's tree is considered. As a consequence, we obtain that the quantity which represents in some sense the number of cuts needed to isolate the root of the tree, is distributed as the height of a leaf picked at random in the Lévy tree.
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Dates et versions

hal-00686569 , version 1 (10-04-2012)
hal-00686569 , version 2 (17-12-2012)

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Romain Abraham, Jean-François Delmas. The forest associated with the record process on a Lévy tree. Stochastic Processes and their Applications, 2013, 123, pp.3497-3517. ⟨hal-00686569v2⟩
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