Joint large deviation result for empirical measures of the near intermediate coloured random geometric graphs

Kwabena Doku-Amponsah

Published 2014-06-12, updated 2015-03-09Version 2

We prove joint large deviation principle for the \emph{ empirical pair measure} and \emph{empirical locality measure} of the \emph{near intermediate} coloured random geometric graph models, see (Canning \& Penman, 2003), on $n$ points picked uniformly in $[0,1]^d,$ for $d\in\N.$ From this result we obtain large deviation principles for the \emph{number of edges per vertex}, the \emph{degree distribution and the proportion of isolated vertices } for the \emph{near intermediate} random geometric graph models.% on $n$ vertices placed uniformly in $[0,1]^d,$ for $d\in\N.$