  We derive the exact equations of motion for the random neighbor version of
the Olami-Feder-Christensen earthquake model in the infinite-size limit. We
solve them numerically, and compare with simulations of the model for large
numbers of sites. We find perfect agreement. But we do not find any scaling or
phase transitions, except in the conservative limit. This is in contradiction
to claims by Lise & Jensen (Phys. Rev. Lett. 76, 2326 (1996)) based on
approximate solutions of the same model. It indicates again that scaling in the
Olami-Feder-Christensen model is only due to partial synchronization driven by
spatial inhomogeneities. Finally, we point out that our method can be used also
for other SOC models, and treat in detail the random neighbor version of the
Feder-Feder model.
