Finite-size effects on extreme events in the BTW model

Anja Garber

MPIPKS, Nonlinear Dynamics and Time Series Analysis, Dresden, Germany

The Abelian sandpile model often used to demonstrate properties of systems showing self-organized criticality is in fact defined on a system of finite size. This results in a modification of key properties for the large events such as the avalanche size probability distribution.

The criticality of the system signifies that avalanches should be independent of each other, implying a Poissonian recurrence time of extreme events. However the finite size of the system leads to a repulsion of extreme events that depends on the avalanche size and not on the respective probability.