Exact solution of the totally asymmetric Oslo model

TL;DR

This paper presents an exact solution to the totally asymmetric Oslo model by computing eigenvectors of its Markov matrix, providing insights into its universality class without relying on scaling assumptions.

Contribution

It introduces a recursive eigenvector method to solve the model exactly, applicable to other stochastic processes as well.

Findings

Exact eigenvectors of the Markov matrix obtained

Solution confirms the universality class of the model

Method applicable to various stochastic systems

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.