| Issue |
Europhys. Lett.
Volume 65, Number 5, March 2004
|
|
|---|---|---|
| Page(s) | 627 - 632 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2003-10165-4 | |
| 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
Received:
23
September
2003
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.