Europhys. Lett.
Volume 65, Number 5, March 2004
Page(s) 627 - 632
Section General
Published online 01 February 2004
Europhys. Lett., 65 (5) , pp. 627-632 (2004)
DOI: 10.1209/epl/i2003-10165-4

Iterated random walk

L. Turban

Laboratoire de Physique des Matériaux, UMR CNRS 7556, Université Henri Poincaré (Nancy 1) - BP 239, 54506 Vandoeuvre lès Nancy Cedex, France

(Received 23 September 2003; accepted in final form 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 $n\rightarrow\infty$, 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.

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.

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