s-Run

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

			(1)
			(2)
			(3)

so

			(4)
			(5)

which is called the mean run count per site or mean run density in percolation theory.

REFERENCES

Finch, S. R. "Percolation Cluster Density Constants." §5.18 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 371-378, 2003.