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

Nathanaël Enriquez (1) , Cyrille Lucas (1) , François Simenhaus (1)

1 MODAL'X - Modélisation aléatoire de Paris X

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.

Mots clés: excursion theory; Sinai's walk; internal DLA; random walks in random environments; excursion theory.

Domaines: Probabilités [math.PR]

Nathanaël Enriquez, Cyrille 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, 2010, 46 (4), pp.991-1000. ⟨hal-00371608⟩