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On The Avalanche-finiteness Of Abelian Sandpiles

S. W. Chan·H. F. Chau
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Abstract

We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than $\mbox{O} \left( N^3 \right)$ arithmetic computations where $N$ is the total number of sites of the system. Key words: Abelian sandpile model; avalanche-finiteness; self-organized criticality

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BibTeXRIS

S. W. Chan, H. F. Chau. 1994-10-17. On The Avalanche-finiteness Of Abelian Sandpiles. https://doi.org/10.1016/0378-4371(95)00079-m

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