Upper and lower bounds for the route length of first-passage percolation in Voronoi tessellations
The first passage percolation defined on a graph obtained from Voronoi tessellation of the plane, generated by a homogeneous Poisson process, is considered. The almost sure existence of the optimal path between arbitrary pair of vertices on the graph (the route for the first-passge time) is proved. This path realizes the infimum of the travel times between vertices. The upper and lower bounds for the route length divided by geometrical distance are proved as well.
upper and lower bounds for the route length
scientific article; zbMATH DE number 579698