On the trajectory of an individual chosen according to supercritical Gibbs measure in the branching random walk
Résumé
Consider a branching random walk on the real line. In a recent article, Chen [9] proved that the renormalised trajectory leading to the leftmost individual at time n converges in law to a standard Brownian excursion. Besides, in [22], Madaule showed the renormalised trajectory of an individual selected according to the critical Gibbs measure converges in law to a Brownian meander. In this article, we prove that trajectory of individuals selected independently according to a supercritical Gibbs measure converge in law to Brownian excursions. Refinements of this results also enables to express the probability for the tra-jectory of two individuals selected according to the Gibbs measure to have split before time t, partially answering a question of [10].
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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