Extreme paths in oriented two-dimensional percolation
2016 ◽
Vol 53
(2)
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pp. 369-380
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Abstract A useful result about leftmost and rightmost paths in two-dimensional bond percolation is proved. This result was introduced without proof in Gray (1991) in the context of the contact process in continuous time. As discussed here, it also holds for several related models, including the discrete-time contact process and two-dimensional site percolation. Among the consequences are a natural monotonicity in the probability of percolation between different sites and a somewhat counter-intuitive correlation inequality.
2017 ◽
Vol E100.C
(10)
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pp. 858-865
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2014 ◽
Vol 118
(24)
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pp. 6466-6474
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1986 ◽
Vol 22
(4)
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pp. 531-542
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1978 ◽
Vol 11
(18)
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pp. L763-L765
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