28 citations · 50 across the 5 of their papers we have counts for
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cond-mat.stat-mech2005★ 14 cited
One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve
M A Stapleton, K Christensen
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 co…
cond-mat.stat-mech2005★ 3 cited
Mean-Field Theory and Sandpile Models
Matthew Stapleton, Kim Christensen
We review and refine the concept of a mean-field theory for the study of sandpile models, which are of central importance in the study of self-organized criticality. By considering…
cond-mat.stat-mech2005★ 4 cited
Universality Class of One-Dimensional Directed Sandpile Models
Matthew Stapleton, Kim Christensen
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 lim…