SUBLOGARITHMIC FLUCTUATIONS FOR INTERNAL DLA

• 成果类型: Article
• 署名作者: Asselah, Amine; Gaudilliere, Alexandre
• 署名单位: Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP735
• 发表日期: 2013
• 页码: 1160-1179
• 关键词: diffusion-limited aggregation

摘要

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of order log(radius) [resp., log(2) (radius)]. Using the same approach, we improve the upper bound on the inner fluctuation to root log(radius) when d is larger than or equal to three. The inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation.