Abelian Sandpiles and Abelian Networks

Abelian Networks are interacting particle systems whose final state does not depend on the order of interactions. A revealing example is the Abelian Sandpile, a model of sand cascading down a pile. We'll see that this model has certain “non-universal” features, and we'll identify "slow mixing" as the culprit: The threshold state of the sandpile retains some memory of its initial state. Then we’ll explore the design space of Abelian Networks in search of a model with more universal features.