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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 $D([0,1],\r)$

Topics:
Branching random walk, spinal decomposition, [
MATH.MATH-PR
]
Mathematics [math]/Probability [math.PR]

Publisher: HAL CCSD

Year: 2013

OAI identifier:
oai:HAL:hal-00827040v1

Provided by:
Hal-Diderot

Downloaded from
https://hal.archives-ouvertes.fr/hal-00827040/document

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