Geodesics in two-dimensional first-passage percolation
The paper concerns the standard first-passage percolation on \(\mathbb{Z}^2\). The passage time \(T(r)\) for a finite path \(r\) defines the random metric \(T(u,v)\) on sites \(u,v\in \mathbb{Z}^2\), which is the infimum of \(T(r)\) over all \(r\) between \(u\) and \(v\). A finite or infinite path \(r\) is called geodesic if each segment \(r(u',v')\) provides \(T(u',v')\). The problem of coalescence of semiinfinite geodesics is considered. A part of the important conjecture that doubly infinite geodesics do not exist is proved.
scientific article; zbMATH DE number 926218