The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 18, Number 2 (2008), 708-746.
Navigation on a Poisson point process
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.
Ann. Appl. Probab., Volume 18, Number 2 (2008), 708-746.
First available in Project Euclid: 20 March 2008
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Bordenave, Charles. Navigation on a Poisson point process. Ann. Appl. Probab. 18 (2008), no. 2, 708--746. doi:10.1214/07-AAP472. https://projecteuclid.org/euclid.aoap/1206018202