Asymptotic Critical Radii in Random Geometric Graphs over 3-Dimensional Convex regions

TL;DR

This paper derives the exact asymptotic distribution of critical radii related to connectivity in 3D random geometric graphs within convex regions, advancing understanding of spatial network thresholds.

Contribution

It provides the first precise asymptotic distribution results for critical radii in 3D convex regions, focusing on k-connectivity and minimum degree.

Findings

Asymptotic distribution formulas for critical radii are established.

Results apply to 3D convex regions, extending previous 2D analyses.

The work enhances theoretical understanding of spatial network connectivity thresholds.

Abstract

This article presents the precise asymptotical distribution of two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, for a random geometry graph distributed over a 3-Dimensional Convex region.