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 &mgr; and sigma are close to 0. We demonstrate that tau-1=&mgr;-sigma=exp-&mgr;(-1)-gamma+ small middle dot small middle dot small middle dot 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 &mgr; 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.