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Branching random walks on binary search trees: convergence of the occupation measure

Published online by Cambridge University Press:  29 October 2010

Eric Fekete
Eric Fekete*
Affiliation:
UVSQ, Département de Mathématiques, 45 av. des États-Unis, 78035 Versailles Cedex, France
*
Corresponding author: fekete@math.uvsq.fr
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Abstract

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.

Keywords

Random binary search treebranching random walkoccupation measurefragmentationrecursive tree
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 14 , 2010 , pp. 286 - 298
Copyright
© EDP Sciences, SMAI, 2010

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