Supercritical behaviors in first-passage percolation

Yu Zhang

Stochastic Processes and their Applications, 1995, vol. 59, issue 2, 251-266

Abstract: We consider standard first passage percolation on Zd: {x(e): e an edge of Zd} is i.i.d. family of random variables with distribution F. Denote by a0,n the first passage time from the origin to (n, 0, ..., 0). We show that there exists a path called a route with passage time a0,n if F(0) > pc. Indeed, we can show that if F(0) > pc, any route of a0,n has to stay in the infinite cluster B with X(e) = 0 except a few edges. We also show that if F(0) > pc, lim Ea0,n = [varrho](F) exists.

Keywords: 60K; 35; First; passage; percolation; Supercriticality (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (1)

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