Shortest Path through Random Points
نویسندگان
چکیده
Let (M, g1) be a compact d-dimensional Riemannian manifold. Let Xn be a set of n sample points in M drawn randomly from a Lebesgue density f . Define two points x, y ∈ M . We prove that the normalized length of the power-weighted shortest path between x, y passing through Xn converges to the Riemannian distance between x, y under the metric gp = f g1, where p > 1 is the power parameter. The result is an extension of the BeardwoodHalton-Hammersley theorem to shortest paths.
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