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.
Mots clés : Sinai's walk, internal DLA, random walks in random environments, excursion theory
@article{AIHPB_2010__46_4_991_0, author = {Enriquez, N. and Lucas, C. and Simenhaus, F.}, title = {The {Arcsine} law as the limit of the internal {DLA} cluster generated by {Sinai's} walk}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {991--1000}, publisher = {Gauthier-Villars}, volume = {46}, number = {4}, year = {2010}, doi = {10.1214/09-AIHP336}, mrnumber = {2744882}, zbl = {1210.82028}, language = {en}, url = {http://www.numdam.org/articles/10.1214/09-AIHP336/} }
TY - JOUR AU - Enriquez, N. AU - Lucas, C. AU - Simenhaus, F. TI - The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2010 SP - 991 EP - 1000 VL - 46 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/09-AIHP336/ DO - 10.1214/09-AIHP336 LA - en ID - AIHPB_2010__46_4_991_0 ER -
%0 Journal Article %A Enriquez, N. %A Lucas, C. %A Simenhaus, F. %T The Arcsine law as the limit of the internal DLA cluster generated by Sinai's walk %J Annales de l'I.H.P. Probabilités et statistiques %D 2010 %P 991-1000 %V 46 %N 4 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/09-AIHP336/ %R 10.1214/09-AIHP336 %G en %F AIHPB_2010__46_4_991_0
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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