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Date: 28-3-2022
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Date: 23-3-2022
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Let be a -vector whose entries are each 1 (with probability ) or 0 (with probability ). An -run is an isolated group of consecutive 1s. Ignoring the boundaries, the total number of runs satisfies
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so
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which is called the mean run count per site or mean run density in percolation theory.
Finch, S. R. "Percolation Cluster Density Constants." §5.18 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 371-378, 2003.
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