1999/08/14 by Supriya Krishnamurthy, S. Krishnamurthy, Anne Tanguy +5 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1209/epl/i2000-00330-9
4 pages LaTex, 3 figures .eps
arxiv created 1999/08/14 · openalex publication_date 2000/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.