A stochastic description of extremal dynamics

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.