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Asymptotic shapes for stationary first passage percolation. (English) Zbl 0852.60104

Summary: This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well-known asymptotic shape result is known to extend to this case. It is easy to give necessary conditions for a compact set \(B \subset \mathbb{R}^d\) to arise as the asymptotic shape for some stationary measure on the passage times. Our main result says that these conditions are also sufficient.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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