On the Rate of Convergence of the Connectivity Threshold of Random Geometric Graphs with Skew Generalized Cantor Distributed Vertices

摘要

In this paper, we study the rate of convergence of the connectivity threshold of random geometric graphs when the underlying distribution of the vertices has no density. We consider n i.i.d. skew generalized Cantor distributed points on [0, 1] and we study the connectivity threshold of a random geometric graph that is built on these points. We show that for this graph, the connectivity threshold converges almost surely to a constant, similar result as in case of symmetric generalized Cantor distributed. We also study the rate of the convergence of this threshold in terms of the $${mathcal L}_1$$ L 1 norm.