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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.
@article{PS_2010__14__286_0,
author = {Fekete, Eric},
title = {Branching random walks on binary search trees : convergence of the occupation measure},
journal = {ESAIM: Probability and Statistics},
pages = {286--298},
publisher = {EDP-Sciences},
volume = {14},
year = {2010},
doi = {10.1051/ps:2008035},
mrnumber = {2779485},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008035/}
}
TY - JOUR AU - Fekete, Eric TI - Branching random walks on binary search trees : convergence of the occupation measure JO - ESAIM: Probability and Statistics PY - 2010 SP - 286 EP - 298 VL - 14 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2008035/ DO - 10.1051/ps:2008035 LA - en ID - PS_2010__14__286_0 ER -
%0 Journal Article %A Fekete, Eric %T Branching random walks on binary search trees : convergence of the occupation measure %J ESAIM: Probability and Statistics %D 2010 %P 286-298 %V 14 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2008035/ %R 10.1051/ps:2008035 %G en %F PS_2010__14__286_0
Fekete, Eric. Branching random walks on binary search trees : convergence of the occupation measure. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 286-298. doi: 10.1051/ps:2008035
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