The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk

N. Enriquez (1) , C. Lucas , François Simenhaus

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We identify the limit of the internal DLA cluster generated by Sinai's walk as the law of a functional of a Brownian motion which turns out to be a new interpretation of the Arcsine law.

Domaines: Probabilités [math.PR]

N. Enriquez, C. Lucas, François Simenhaus. The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2011, 46 (4), pp.991-1000. ⟨10.1214/09-AIHP336⟩. ⟨hal-00559451⟩