Scaling limit of the path leading to the leftmost particle in a branching random walk
Résumé
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 $D([0,1],\r)$.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)