Branching random walks on binary search trees : convergence of the occupation measure
ESAIM: Probability and Statistics, Tome 14 (2010), pp. 286-298

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.

DOI : 10.1051/ps:2008035
Classification : 60F05, 60G50, 68W40, 60J80, 05C05
Keywords: random binary search tree, branching random walk, occupation measure, fragmentation, recursive tree 
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     author = {Fekete, Eric},
     title = {Branching random walks on binary search trees : convergence of the occupation measure},
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     publisher = {EDP Sciences},
     volume = {14},
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     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps:2008035/}
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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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