Exact solution of the anisotropic Bak-Sneppen model in one dimension

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents $\tau$ and $\mu=d/D$, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. Our central result is the solution of the anisotropic Bak-Sneppen model in one dimension based on an exact equation for the distribution of avalanche spatial sizes. We derive the exact value $\gamma=2$ for one of the critical exponents of the model and determine other critical exponents 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.