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A Stochastic Description for Extremal Dynamics

S. Krishnamurthy·A. Tanguy·P. Abry·S. Roux
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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.

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S. Krishnamurthy, A. Tanguy, P. Abry, S. Roux. 1999-08-14. A Stochastic Description for Extremal Dynamics. https://doi.org/10.1209/epl%2Fi2000-00330-9

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