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Let a random (0,1)-matrix have entries which are 1 (with probability
) or 0 (with probability
) and numbers are assigned to the edges of a grid. A
-cluster is an isolated group of
adjacent (i.e., horizontally or vertically connected) 1s. Let
be the total number of "bond" clusters, then
exists. The analytic value is known for ,
(OEIS A086269; Ziff et al. 1997).
Finch, S. R. "Percolation Cluster Density Constants." §5.18 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 371-378, 2003.
Sloane, N. J. A. Sequence A086269 in "The On-Line Encyclopedia of Integer Sequences.
"Ziff, R. M.; Finch, S. R.; and Adamchik, V. S. "Universality of Finite-Sized Corrections to the Number of Critical Percolation Clusters." Phys. Rev. Let. 79, 3447-3450, 1997.
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