Abstract
GIVEN a lattice of m × n points, suppose that each may be ‘black’ or ‘white’ with probabilities p and q = 1 â p. The probability distribution of the number of ‘black-white’ joins is then of interest in several branches of science1,2,3. The expected number is 2pq (2mnâmân.) and the second moment about the mean is 2pq (8mnâ7mâ7n+4) + 4p2q2 (13m+13nâ14mnâ8).
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Mood, A. M., Ann. Math. Stat., 11, 367 (1940).
Ising, E., Z. Phys., 31, 253 (1925).
Wishart, J., and Hirschfeld, H. O., J. Lond. Math. Soc., 11, 227 (1937).
Bernstein, S., Math. Ann., 97, 1 (1926).
Levene, H., Bull. Amer. Math. Soc., 52, 621 (1946).
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MORAN, P. Random Associations on a Lattice. Nature 158, 521 (1946). https://doi.org/10.1038/158521b0
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DOI: https://doi.org/10.1038/158521b0
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