Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-12-23
Physics
Condensed Matter
Statistical Mechanics
24 pages, 5 figures
Scientific paper
10.1088/0305-4470/39/29/007
We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the Totally Asymmetric Oslo model, thereby identifying a large universality class of directed sandpiles. We map the avalanche size to the area under a Brownian curve with an absorbing boundary at the origin, motivating us to solve this Brownian curve problem. Thus, we are able to determine the moment generating function for the avalanche-size probability in this universality class, explicitly calculating amplitudes of the leading order terms.
Christensen Kim
Stapleton M. A.
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