Document Zbl 0866.60087

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On the non-convexity of the time constant in first-passage percolation. (English) Zbl 0866.60087

Electron. Commun. Probab. 1, paper 1, 1-6 (1996).

J. M. Hammersley and D. J. A. Welsh [in: Bernoulli-Bayes-Laplace Anniversary Vol., 61-110 (1965; Zbl 0143.40402)] conjectured that in (Bernoulli) edge percolation on \(Z^d\) the time constant \(\mu= \mu(F)\) is a convex function of the distribution function \(F\) of the passage time \(t(e) \geq 0\) of an edge \(e\) provided \(t(e)\) is integrable. In the present paper an example is given for which convexity of the time constant does not hold.

Reviewer: K.Schürger (Bonn)

Cited in 2 Documents

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82B05	Classical equilibrium statistical mechanics (general)

Keywords:

edge percolation; passage time

Citations:

Zbl 0143.40402

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