Levy-nearest-neighbors Bak-Sneppen model

We study a random neighbor version of the Bak-Sneppen model, where ``nearest neighbors'' are chosen according to a probability distribution decaying as a power law of the distance from the active site, P(x)~\|x-x_ac\|^-ω. All of the exponents characterizing the self-organized critical state of this model depend on the exponent ω. As ω-->1 we recover the usual random nearest-neighbor version of the model. The pattern of results obtained for a range of values of ω is also compatible with the results of simulations of the original BS model in high dimensions. Moreover, our results suggest a critical dimension d_c=6 for the Bak-Sneppen model, in contrast with previous claims.