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

Kwabena Doku-Amponsah

doi:10.1186/s40064-016-2718-z

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

Kwabena Doku-Amponsah

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	1140
Journal	SpringerPlus
Volume	5
Issue number	1
DOIs	https://doi.org/10.1186/s40064-016-2718-z
Publication status	Published - 1 Dec 2016

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

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10.1186/s40064-016-2718-z

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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.",

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AB - 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.

KW - Coloured random geometric graph

KW - Degree distribution

KW - Empirical measure

KW - Empirical pair measure

KW - Entropy

KW - Erdős–Rényi graph

KW - Isolated vertices

KW - Joint large deviation principle

KW - Random geometric graph

KW - Relative entropy

KW - Typed graph

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

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