Exact solution of the totally asymmetric Oslo model

Abstract

Recently it has been found [G. Pruessner and H. J. Jensen, Phys. Rev. Lett. 91, 244303 (2003)] that a totally asymmetric variant of the Oslo model [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)] represents the entire universality class of the Oslo model with anisotropy. The totally asymmetric model can be solved without scaling assumptions by finding recursively the eigenvectors of the Markov matrix, which can be suitably modified to produce the moment generating function of the relevant observable. This method should be applicable to many other stochastic processes.