The density of interfaces: a new first-passage problem
Keyword(s):
We introduce and study a novel type of first-passage percolation problem on where the associated first-passage time measures the density of interface between two types of sites. If the types, designated + and –, are independently assigned their values with probability p and (1 — p) respectively, we show that the density of interface is non-zero provided that both species are subcritical with regard to percolation, i.e. pc > p > 1 – pc. Furthermore, we show that as p ↑ pc or p ↓ (1 – pc), the interface density vanishes with scaling behavior identical to the correlation length of the site percolation problem.
1993 ◽
Vol 30
(04)
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pp. 851-862
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2020 ◽
Vol 57
(1)
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pp. 221-236
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1977 ◽
Vol 9
(01)
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pp. 38-54
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1976 ◽
Vol 13
(02)
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pp. 290-300
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2011 ◽
Vol 20
(3)
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pp. 435-453
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Keyword(s):
2013 ◽
Vol 5
(4)
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pp. 334