Details

Autor(en) / Beteiligte

• Iyer, Srikanth K.
• Thacker, Debleena

Titel

NONUNIFORM RANDOM GEOMETRIC GRAPHS WITH LOCATION-DEPENDENT RADII

Ist Teil von

• The Annals of applied probability, 2012-10, Vol.22 (5), p.2048-2066

Ort / Verlag

Hayward: Institute of Mathematical Statistics

Erscheinungsjahr

2012

Quelle

Project Euclid Complete

Beschreibungen/Notizen

• We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function nf(.), where n ε ℕ, and f is a probability density function on ℝ d . A vertex located at x connects via directed edges to other vertices that are within a cut-off distance r n (x). We prove strong law results for (i) the critical cut-off function so that almost surely, the graph does not contain any node with out-degree zero for sufficiently large n and (ii) the maximum and minimum vertex degrees. We also provide a characterization of the cut-off function for which the number of nodes with out-degree zero converges in distribution to a Poisson random variable. We illustrate this result for a class of densities with compact support that have at most polynomial rates of decay to zero. Finally, we state a sufficient condition for an enhanced version of the above graph to be almost surely connected eventually.