The Shape Theorem for the Frog Model
The Shape Theorem for the Frog Model
复制标题
青蛙模型的形状定理
DOI：
10.1214/aoap/1026915614
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
S. Popov
中科院分区：
文献类型：
--
作者：
O. Alves;F. Machado;S. Popov
我们证明了Zd上一个简单随机漫步的增长集的形状定理，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。当一个沉睡的粒子被一个活跃的粒子撞击时，它也会变得活跃起来。在时刻0，所有的粒子都处于睡眠状态，除了位于原点的粒子。我们证明了所有活动粒子的原始位置集合，经过时间的调整，收敛于某个紧致凸集。
We prove a shape theorem for a growing set of simple random walks on Zd, known as the 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, it becomes active too. At time 0 all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all active particles, rescaled by the elapsed time, converges to some compact convex set.