Volume 51, Number 1, July I 2000
|Page(s)||1 - 7|
|Published online||01 September 2002|
A stochastic description of extremal dynamics
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
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
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