A Stochastic Description for Extremal Dynamics
arXiv:cond-mat/9908212 · doi:10.1209/epl/i2000-00330-9
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.
4 pages LaTex, 3 figures .eps