One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve
Statistical Mechanics
2009-11-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0512622,
title = {One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve},
author = {M A Stapleton and K Christensen},
journal= {arXiv preprint arXiv:cond-mat/0512622},
year = {2009}
}
Comments
24 pages, 5 figures