Sublogarithmic fluctuations for internal DLA
Sublogarithmic fluctuations for internal DLA
复制标题
内部 DLA 的亚对数波动
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
A. Gaudilliere
中科院分区：
文献类型：
--
作者：
A. Asselah;A. Gaudilliere
我们考虑内部扩散限制维度大于或等于 2 的聚合。这是一种随机簇增长模型，其中随机游走从 d 维晶格的原点开始，一次一个，并在到达未被先前游走占据的位置时停止移动。已知星团的渐进形状是球体。当维度为二维或更多时，我们在之前的论文中已经证明，其半径的内（或外）波动最多为 log(radius) [resp., log2(radius)] 阶。使用相同的方法，当 d 大于或等于 3 时，我们将内部波动的上限改进为 log(radius)−−−−−−−−√。然后使用内部波动来获得外部波动的类似上限。
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., log2(radius)]. Using the same approach, we improve the upper bound on the inner fluctuation to 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.