The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk
Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 4, pp. 991-1000.

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.

On détermine la loi limite du cluster de diffusion à agrégation limitée interne comme celle d'une fonctionnelle du mouvement brownien, qui donne une nouvelle interprétation de la loi de l'Arcsinus.

DOI: 10.1214/09-AIHP336
Classification: 60K37,  60F05
Keywords: Sinai's walk, internal DLA, random walks in random environments, excursion theory
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Enriquez, N.; Lucas, C.; Simenhaus, F. The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk. Annales de l'I.H.P. Probabilités et statistiques, Volume 46 (2010) no. 4, pp. 991-1000. doi : 10.1214/09-AIHP336. http://www.numdam.org/articles/10.1214/09-AIHP336/

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