Asymptotic properties of Euclidean shortest-path trees in random geometric graphs

Christian Hirsch, David Neuhäuser, Catherine Gloaguen and Volker Schmidt

Statistics & Probability Letters, 2015, vol. 107, issue C, 122-130

Abstract: We consider asymptotic properties of two functionals on Euclidean shortest-path trees appearing in random geometric graphs in R2 which can be used, for example, as models for fixed-access telecommunication networks. First, we determine the asymptotic bivariate distribution of the two backbone lengths inside a certain class of typical Cox–Voronoi cells as the size of this cell grows unboundedly. The corresponding Voronoi tessellation is generated by a stationary Cox process which is concentrated on the edges of the random geometric graph and whose intensity tends to 0. The limiting random vector can be represented as a simple geometric functional of a decomposition of a typical Poisson–Voronoi cell induced by an independent random sector. Using similar methods, we consider the asymptotic bivariate distribution of the total lengths of the two subtrees inside the Cox–Voronoi cell.

Keywords: Random geometric graph; Cox process; Voronoi tessellation; Shortest-path tree; Backbone length; Total length (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.08.012

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