Abstract
The behaviour of the percolation process on Ld depends dramatically on whether p < p c or p > p c . In the former subcritical case, all open clusters are almost surely finite and their size-distribution has a tail which decays exponentially. In the latter supercritical case, there exists almost surely an infinite open cluster and the size-distribution of the remaining finite open clusters has a tail which decays slower than exponentially. Some of the major differences between these two phases are highlighted in the following table.
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Grimmett, G. (1989). Near the Critical Point: Scaling Theory. In: Percolation. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4208-4_7
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DOI: https://doi.org/10.1007/978-1-4757-4208-4_7
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