具有随机初始构形青蛙模型的形状定理
The shape theorem for the frog model with random initial configuration
摘要：
本文证明了Z^d上增长的简单随机游动集的形状定理，称为青蛙模型。这个过程的动力学描述如下：有活动粒子，它们执行独立的离散时间SRW，和睡眠粒子，它们不移动。当一个休眠的粒子被一个活跃的粒子击中时，前者也会变得活跃。最初，将随机数的颗粒放入每个位点。在时间0，所有粒子都在睡眠，除了那些放置在原点的粒子。我们证明了活动粒子所访问的所有站点的集合，经过时间的重新标度，收敛到一个紧的凸集。
英文摘要：
We prove a shape theorem for a growing set of simple random walks on Z^d, known as frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, the former becomes active as well. Initially, a random number of particles is placed into each site. At time 0 all particles are sleeping, except for those placed at the origin. We prove that the set of all sites visited by active particles, rescaled by the elapsed time, converges to a compact convex set.
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。
