Scaling limit of the path leading to the leftmost particle in a branching random walk

Abstract : We consider a discrete-time branching random walk defined on the real line, which is assumed to be supercritical and in the boundary case. It is known that its leftmost position of the $n$-th generation behaves asymptotically like $\frac{3}{2}\ln n$, provided the non-extinction of the system. The main goal of this paper, is to prove that the path from the root to the leftmost particle, after a suitable normalizatoin, converges weakly to a Brownian excursion in $D([0,1],\r)$.
Keywords :
Type de document :
Pré-publication, Document de travail
2013
Domaine :

https://hal.archives-ouvertes.fr/hal-00827040
Contributeur : Xinxin Chen <>
Soumis le : mardi 28 mai 2013 - 18:02:31
Dernière modification le : jeudi 27 avril 2017 - 09:46:22
Document(s) archivé(s) le : jeudi 29 août 2013 - 09:10:07

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article-2-3rd-version.pdf
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Identifiants

• HAL Id : hal-00827040, version 1
• ARXIV : 1305.6723

Citation

Xinxin Chen. Scaling limit of the path leading to the leftmost particle in a branching random walk. 2013. <hal-00827040>

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