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

TL;DR

This paper establishes a joint large deviation principle for empirical measures in coloured random geometric graphs, enabling analysis of various graph properties in high-dimensional probabilistic models.

Contribution

It introduces a joint large deviation framework for empirical measures in coloured random geometric graphs, extending understanding of their probabilistic behavior.

Findings

Large deviation principles for edge count per vertex

Degree distribution deviations quantified

Proportion of isolated vertices analyzed

Abstract

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 on $n$ points picked uniformly in a $d-$dimensional torus of a unit circumference.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.