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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. |