Abstract
On a locally finite point set, a navigation defines a path through the point set from one point to another. The set of paths leading to a given point defines a tree known as the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on ℝd. We examine the local weak convergence of the navigation tree, the asymptotic average of a functional along a path, the shape of the navigation tree and its topological ends. We illustrate our work in the small-world graphs where new results are established.
Citation
Charles Bordenave. "Navigation on a Poisson point process." Ann. Appl. Probab. 18 (2) 708 - 746, April 2008. https://doi.org/10.1214/07-AAP472
Information