Abelian Networks

In order to explain self-organized criticality Dhar developed a theory of abelian networks that was formalized by Bond and Levine. I will describe this theory and show that it contains some of the most common mathematical models for self-organized criticality. These models are all believed to have critical exponents. I will talk about one particular abelian network known as oil and water. I will explain why I think that it is an abelian network where we have some chance of calculating these critical exponents.