Issue |
Europhys. Lett.
Volume 51, Number 1, July I 2000
|
|
---|---|---|
Page(s) | 1 - 7 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2000-00330-9 | |
Published online | 01 September 2002 |
A stochastic description of extremal dynamics
1
LPMMH, Ecole Supérieure de Physique et de Chimie
Industrielles 10 rue Vauquelin, 75231 Paris, France
2
CNRS UMR 5586, Université Lyon I - 43,
bvd. du 11 Novembre 1918 69622 Villeurbanne, France
3
CNRS UMR 5672, ENS Lyon - 46, allée d'Italie
69364 Lyon Cedex 07, France
4
Laboratoire Surface du Verre et Interfaces, UMR
CNRS/Saint-Gobain 39, Quai Lucien Lefranc,
F-93303 Aubervilliers Cedex, France
Received:
22
February
2000
Accepted:
10
May
2000
We show that extremal dynamics is very well described by the “Linear Fractional Stable Motion” (LFSM), a stochastic process entirely defined by two exponents that take into account spatio-temporal correlations in the distribution of active sites. We demonstrate this numerically and analytically using well-known properties of the LFSM. Further, we use this correspondence to show new results, such as an exact expression for an n-point correlation function as well as an equation of fractional order for interface growth in extremal dynamics.
PACS: 02.50.Ey – Stochastic processes / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.65.+b – Self-organized systems
© EDP Sciences, 2000
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.