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Geodesics in first passage percolation. (English) Zbl 1153.60055
The so-called first passage percolation process has been introduced in the form of a time-dependent model to describe the passage of a fluid through a porous medium. Loosely speaking, the passage time \(\tau(x,y)\) from a state \(x\) to a state \(y\) is thought of as a geometrical distance therefore the concept of (time) geodesic. It is shown that for a very general class of first passage percolation processes, there exist almost surely at least four disjoint infinite geodesics. Related results are stated for the Richardson’s spatial growth models.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
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