Mean-Field Theory and Sandpile Models

Abstract

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 the simple one-dimensional random walker with an absorbing and reflecting boundary we are able to construct a complete mean-field picture which we can solve in detail for different types of driving. Using this theory, we are able to clarify the effect of finite driving rate on sandpile models, as well as the observed sensitivity of certain universal quantities on the driving.