We study the Bak-Sneppen model in the probabilistic framework of the run time statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing self-organized criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanches of activity power law distributed. In this Letter we use the RTS approach to compute the value of $x_c$, the value of the avalanche exponent $\tau$, and the asymptotic distribution of minimal fitnesses.

• Received 27 October 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.1896