Boundary effects in a random neighbor model of earthquakes

We introduce spatial inhomogeneities (boundaries) in a random neighbor version of the Olami, Feder and Christensen model [Phys. Rev. Lett. 68, 1244 (1992)] and study the distributions of avalanches starting both from the bulk and from the boundaries of the system. Because of their clear geophysical interpretation, two different boundary conditions have been considered (named free and open, respectively). In both cases the bulk distribution is described by the exponent $\tau \simeq {3/2}$. Boundary distributions are instead characterized by two different exponents $\tau ' \simeq {3/2}$ and $\tau ' \simeq {7/4}$, for free and open boundary conditions, respectively. These exponents indicate that the mean-field behavior of this model is correctly described by a recently proposed inhomogeneous form of critical branching process.