Critical exponents of the anisotropic Bak-Sneppen model

We analyze the behavior of the spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents $\ensuremath{\tau}$ and $\ensuremath{\mu}=d/D,$ recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For the one-dimensional anisotropic Bak-Sneppen model, we derive an exact equation for the distribution of avalanche spatial sizes, and extract the value $\ensuremath{\gamma}=2$ for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation.