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

Eric Fekete

ESAIM: Probability and Statistics (2010)

  • Volume: 14, page 286-298
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Fekete, Eric. "Branching random walks on binary search trees: convergence of the occupation measure." ESAIM: Probability and Statistics 14 (2010): 286-298. <http://eudml.org/doc/250822>.

@article{Fekete2010,
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. },
author = {Fekete, Eric},
journal = {ESAIM: Probability and Statistics},
keywords = {Random binary search tree; branching random walk; occupation measure; fragmentation; recursive tree; random binary search tree},
language = {eng},
month = {10},
pages = {286-298},
publisher = {EDP Sciences},
title = {Branching random walks on binary search trees: convergence of the occupation measure},
url = {http://eudml.org/doc/250822},
volume = {14},
year = {2010},
}

TY - JOUR
AU - Fekete, Eric
TI - Branching random walks on binary search trees: convergence of the occupation measure
JO - ESAIM: Probability and Statistics
DA - 2010/10//
PB - EDP Sciences
VL - 14
SP - 286
EP - 298
AB - 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.
LA - eng
KW - Random binary search tree; branching random walk; occupation measure; fragmentation; recursive tree; random binary search tree
UR - http://eudml.org/doc/250822
ER -

References

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