Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155519 | Stochastic Processes and their Applications | 2013 | 21 Pages |
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 of Addario-Berry, Broutin and Holmgren where only Aldous's tree is considered. As a consequence, we obtain that the “average pruning time” of a leaf is distributed as the height of a leaf picked at random in the Lévy tree.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Romain Abraham, Jean-François Delmas,