title: Joint large deviation result for empirical measures of the coloured random geometric graphs.
abstract: We prove joint large deviation principle for the empirical pair measure and empirical locality measure of the near intermediate coloured random geometric graph models on n points picked uniformly in a d-dimensional torus of a unit circumference. From this result we obtain large deviation principles for the number of edges per vertex, the degree distribution and the proportion of isolated vertices for the near intermediate random geometric graph models.
authors: Statistics Department, University of Ghana, Box LG 115, Legon, Ghana.
authors: Kwabena
authors: 0000-0003-1638-0936
authors: K
authors: Doku-Amponsah
keywords: Coloured random geometric graph; Degree distribution; Empirical measure; Empirical pair measure; Entropy; Erdős–Rényi graph; Isolated vertices; Joint large deviation principle; Random geometric graph; Relative entropy; Typed graph