Z^d中转子-路由器模型的球渐近性
Spherical Asymptotics for the Rotor-Router Model in Z^d
摘要：
转子路由器模型是由Jim Propp发明的随机游动的确定性模拟。它可以用来定义一个类似于内扩散限制聚集的确定性聚集模型。我们证明了简单随机游动从Z^d中的有限区域的退出时间的等周不等式，并利用它证明了Z^d中的转子-路由器聚集模型的形状，适当地重新缩放，收敛到R^d中的欧几里得球。
英文摘要：
The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to define a deterministic aggregation model analogous to internal diffusion limited aggregation. We prove an isoperimetric inequality for the exit time of simple random walk from a finite region in Z^d, and use this to prove that the shape of the rotor-router aggregation model in Z^d, suitably rescaled, converges to a Euclidean ball in R^d.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
