Moderate Deviations for Shortest-path Lengths on Random Segment Processes
نویسندگان
چکیده
We consider first-passage percolation on segment processes and provide concentration results concerning moderate deviations of shortest-path lengths from a linear function in the distance of their endpoints. The proofs are based on a martingale technique developed by H. Kesten for an analogous problem on the lattice. Our results are applicable to graph models from stochastic geometry. For example, they imply that the time constant in Poisson-Voronoi and Poisson-Delaunay tessellations is strictly greater than 1. Furthermore, applying the framework of Howard and Newman, our results can be used to study the geometry of geodesics in planar shortest-path trees. 1991 Mathematics Subject Classification. 60D05, 05C80, 82B43. dates will be set by the publisher.
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