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The forest associated with the record process on a Lévy tree

Abstract : 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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Contributor : Romain Abraham <>
Submitted on : Monday, December 17, 2012 - 9:55:57 AM
Last modification on : Friday, May 4, 2018 - 1:17:29 AM
Long-term archiving on: : Sunday, December 18, 2016 - 2:43:27 AM


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  • HAL Id : hal-00686569, version 2
  • ARXIV : 1204.2357



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



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