The forest associated with the record process on a Levy tree

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Abraham, Romain¹  Delmas, Jean-Francois² 

[1] Univ Orleans, CNRS, Lab MAPMO, UMR 7349,FR 2964, F-45067 Orleans 2, France

[2] Univ Paris Est, Cerm ENPC, F-77455 Marne La Vallee, France

关键词: Levy tree;    Continuum random tree;    Records;    Cutting down a tree;   

DOI  :  10.1016/j.spa.2013.04.017

来源: Elsevier

【 摘 要 】

We perform a pruning procedure on a Levy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the Levy tree). We prove that the tree constructed by regrafting is distributed as the original Levy 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 Levy tree. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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