Matthew Stapleton, Kim Christensen
Published 2005-06-29Version 1
A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.
Comments: 4 pages, 2 figures
One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve
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