Perturbative approach to the Bak-Sneppen model

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.