Exact solution of the totally asymmetric Oslo model

2004/02/23 by Gunnar Pruessner · 1 citation
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1088/0305-4470/37/30/005

published as J. Phys. A: Math. Gen. 37 (30), 7455--7471 (2004) · 19 pages, 3 figures, JPA style

arxiv created 2004/02/23 · openalex publication_date 2004/07/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Recently it has been found (Pruessner G and Jensen H J 2003 Phys. Rev. Lett. 91 244303) that a totally asymmetric variant of the Oslo model (Christensen K et al 1996 Phys. Rev. Lett. 77 107) 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.

Citations

• Non-equilibrium critical phenomena and phase transitions into absorbing states

Cited by

• An explicit formula of the Oslo stationary state

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