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, Tome 46 (2010) no. 4, pp. 991-1000.

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.

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.

DOI : 10.1214/09-AIHP336
Classification : 60K37, 60F05
Mots-clés : Sinai's walk, internal DLA, random walks in random environments, excursion theory 
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     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
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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, Tome 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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