Lower bounds on 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); Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0476-6
• 发表日期: 2014
• 页码: 39-53
• 关键词: diffusion-limited aggregation

摘要

We consider internal diffusion limited aggregation in dimension two or more. This is a random cluster growth model, where random walks start at the origin of the lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. When random walks are sent from the origin, we establish a lower bound for the inner and outer errors fluctuations of order square root of the logarithm of . When dimension is three or more, this lower bound matches the upper bound recently obtained in independent works of Asselah and GaudilliSre (Ann Prob arXiv:1011.4592, 2010) and Jerison et al. (Internal DLA and the Gaussian free field arXiv:1012.3453, 2010). Also, we produce as a corollary of our proof of Asselah and GaudilliSre (Ann Prob arXiv:1011.4592, 2010), an upper bound for the fluctuation of the inner error in a specified direction.