Iterated random walk
Statistical Mechanics
2007-05-23 v1
Abstract
The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using the method of moments. When the number of iterations goes to infinity, a time-independent asymptotic density is obtained. It has a simple symmetric exponential form which is stable against the modification of a finite number of iterations. When n is large, the deviation from the stationary density is exponentially small in n. The continuum results are compared to Monte Carlo data for the discrete iterated random walk.
Cite
@article{arxiv.cond-mat/0312358,
title = {Iterated random walk},
author = {L. Turban},
journal= {arXiv preprint arXiv:cond-mat/0312358},
year = {2007}
}
Comments
7 pages, 2 figures