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The density of interfaces: a new first-passage problem

  • L. Chayes (a1) and C. Winfield (a1)

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 ppc or p ↓ (1 – p c), the interface density vanishes with scaling behavior identical to the correlation length of the site percolation problem.

Corresponding author
Postal address for both authors: Department of Mathematics, University of California, Los Angeles, CA 90024, USA.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
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