A Stochastic Description for Extremal Dynamics
Disordered Systems and Neural Networks
2009-10-31 v1
Abstract
We show that extremal dynamics is very well modelled 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 write an exact expressions for an n-point correlation function as well as an equation of fractional order for interface growth in extremal dynamics.
Cite
@article{arxiv.cond-mat/9908212,
title = {A Stochastic Description for Extremal Dynamics},
author = {S. Krishnamurthy and A. Tanguy and P. Abry and S. Roux},
journal= {arXiv preprint arXiv:cond-mat/9908212},
year = {2009}
}
Comments
4 pages LaTex, 3 figures .eps