Bak-Sneppen model near zero dimension

We consider the Bak-Sneppen model near zero dimension, where the avalanche exponent tau is close to 1 and the exponents mu, and sigma are close to 0. We demonstrate that tau - 1 = mu - sigma= exp{-mu(-1)- gamma+...} in this limit, where gamma is Euler's constant. The avalanche hierarchy equation is rewritten in a form that makes it possible to find the relation between the critical exponents sigma and mu. with high accuracy. We obtain precise values of the critical exponents for the one and two-dimensional Bak-Sneppen model and for the one-dimensional anisotropic Bak-Sneppen model.