Navigation on a Poisson Point Process
نویسنده
چکیده
On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on R. 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. AMS Classification: Primary 60D05, 05C05 ; secondary 90C27, 60G55.
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Navigation on a Poisson
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 R. We examine the local weak convergence of the navigation tree, the asymptotic average...
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