一类自回避型随机游动的漂移速度

考虑一种直线上的随机游动模型:边的权重根据随机游动者的经过次数而相应递减.我们考察这个过程中随机游动者的漂移速度,讨论了随机游动者的位置与步数的关系.利用计算机模拟得到数据进行拟合,定量地确定出变量之间的关系.在某种条件下,随机游动者的位置的对数与步数的对数之比是一定的,不会随着边的权值递减的快慢不同而发生改变.这一点是值得进一步考虑的.

The Drift Velocity of a Special Type of Self-Avoiding Random Walk

We address the problem of a special type of self-avoiding random walk,the weight of whose edge decreases when the edge is traversed.By exploring the relation between the step and the walker′s position,we obtain some conclusions concerning the drift velocity.The approach has three components: simulating the process,fitting a curve,and quantifying the relation.The ratio of the position′s logarithm and the step′s logarithm is nearly constant under some circumstances,which indicates a property of universality with regard to the drift velocity.