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The forest associated with the record process on a L\'evy tree
- Source :
- Stochastic Processes and their Applications 123 (2013) 3497-3517
- Publication Year :
- 2012
-
Abstract
- We perform a pruning procedure on a L\'evy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the L\'evy tree). We prove that the tree constructed by regrafting is distributed as the original L\'evy 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 L\'evy tree.
- Subjects :
- Mathematics - Probability
Subjects
Details
- Database :
- arXiv
- Journal :
- Stochastic Processes and their Applications 123 (2013) 3497-3517
- Publication Type :
- Report
- Accession number :
- edsarx.1204.2357
- Document Type :
- Working Paper