Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

Abstract

We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jump over holes of $\le k$ sites. An analytic calculation shows that not only the size distribution of forest clusters but also the size distribution of fires is characterized by the same critical exponent as in the nearest-neighbor model, i.e. the critical behavior of the model is universal. Computer simulations confirm the analytic results.