Randomized Random Walk on a Random Walk

摘要

This paper discusses generalizations of the model introduced by Kehr and Kunter of the random walk of a particle on a one-dimensional chain which in turn has been constructed by a random walk procedure. The superimposed random walk is randomised in time according to the occurrences of a stochastic point process. The probability of finding the particle in a particular position at a certain instant is obtained explicitly in the transform domain. It is found that the asymptotic behaviour for large time of the mean-square displacement of the particle depends critically on the assumed structure of the basic random walk, giving a diffusion-like term for an asymmetric walk or a square root law if the walk is symmetric. Many results are obtained in closed form for the Poisson process case, and these agree with those given previously by Kehr and Kunter. (Atomindex citation 15:007267)