On a Lower Bound for the Time Constant of First-passage Percolation
نویسندگان
چکیده
We consider the Bernoulli first-passage percolation on Z (d ≥ 2). That is, the edge passage time is taken independently to be 1 with probability 1− p and 0 otherwise. Let μ(p) be the time constant. We prove in this paper that μ(p1)− μ(p2) ≥ μ(p2) 1− p2 (p2 − p1) for all 0 ≤ p1 < p2 < 1 by using Russo’s formula. AMS classification: 60K 35. 82B 43.
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