The dimension of loop-erased random walk in 3D
The dimension of loop-erased random walk in 3D
复制标题
3D 循环擦除随机游走的维度
DOI：
10.1103/physreve.82.062102
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
D. Wilson
中科院分区：
文献类型：
--
作者：
D. Wilson
Loop-erased random walk（英语：Loop-erased random walk）是由Lawler提出的一种随机路径，它是通过在随机路径中擦除循环而得到的。均匀随机生成树中连接点的路径分布为环擦除随机游走[1-3]。均匀生成树反过来又与自组织临界性的阿贝尔沙堆模型密切相关[4]，并且环擦除随机行走的性质在这些沙堆的雪崩中表现出来。特别地，LERW的分维z与沙堆模型中的倾倒的标度行为有关[5，6]。
Loop-erased random walk (LERW) is the path obtained from a random walk by erasing loops as they are formed, and was introduced by Lawler. The paths connecting points in a uniformly random spanning tree are distributed as loop-erased random walk [1–3]. Uniform spanning trees in turn are closely related to the abelian sandpile model of self-organized criticality [4], and properties of loop-erased random walk manifest themselves in the avalanches of these sandpiles. In particular, the fractal dimension z of LERW is related to the scaling behavior of topplings in the sandpile models [5, 6].