Häggström, Olle; Meester, Ronald Asymptotic shapes for stationary first passage percolation. (English) Zbl 0852.60104 Ann. Probab. 23, No. 4, 1511-1522 (1995). 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. Cited in 21 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory Keywords:first passage percolation; asymptotic shape; subadditivity PDFBibTeX XMLCite \textit{O. Häggström} and \textit{R. Meester}, Ann. Probab. 23, No. 4, 1511--1522 (1995; Zbl 0852.60104) Full Text: DOI