Volume 14, 2010
|Page(s)||286 - 298|
|Published online||29 October 2010|
Branching random walks on binary search trees: convergence of the occupation measure
UVSQ, Département de Mathématiques, 45 av. des États-Unis, 78035 Versailles Cedex, France
Corresponding author: Corresponding author: firstname.lastname@example.org
Revised: 13 November 2007
Revised: 16 October 2008
We consider branching random walks with binary search trees as underlying trees. We show that the occupation measure of the branching random walk, up to some scaling factors, converges weakly to a deterministic measure. The limit depends on the stable law whose domain of attraction contains the law of the increments. The existence of such stable law is our fundamental hypothesis. As a consequence, using a one-to-one correspondence between binary trees and plane trees, we give a description of the asymptotics of the profile of recursive trees. The main result is also applied to the study of the size of the fragments of some homogeneous fragmentations.
Mathematics Subject Classification: 60F05 / 60G50 / 68W40 / 60J80 / 05C05
Key words: Random binary search tree / branching random walk / occupation measure / fragmentation / recursive tree
© EDP Sciences, SMAI, 2010
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