The forest associated with the record process on a Lévy tree |
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Authors: | Romain Abraham Jean-François Delmas |
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Institution: | 1. Laboratoire MAPMO, CNRS, UMR 7349, Fédération Denis Poisson, FR 2964, Université d’Orléans, B.P. 6759, 45067 Orléans cedex 2, France;2. Université Paris-Est, Cermics (ENPC), 77455 Marne-la-Vallée, France |
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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. |
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Keywords: | 60J80 60C05 |
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