Perturbative approach to the Bak-Sneppen model

We study the Bak-Sneppen model in the probabilistic framework of the run ti me statistics (RTS). This model has attracted a large interest for its simp licity being a prototype for the whole class of models showing self-organiz ed criticality. The dynamics is characterized by a self-organization of alm ost all the species fitnesses above a nontrivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in avalanc hes of activity power law distributed. In this Letter we use the RTS approa ch to compute the value of x(c), the value of the avalanche exponent tau, a nd the asymptotic distribution of minimal fitnesses.