Volume 65, Number 5, March 2004
|Page(s)||627 - 632|
|Published online||01 February 2004|
Iterated random walk
Laboratoire de Physique des Matériaux, UMR CNRS 7556, Université Henri Poincaré (Nancy 1) - BP 239, 54506 Vandœuvre lès Nancy Cedex, France
Accepted: 15 December 2003
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 , 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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics / 66.30.-h – Diffusion in solids
© EDP Sciences, 2004
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