On the Probability of the Existence of Fixed-Size Components in Random Geometric Graphs

TL;DR

This paper derives precise asymptotic probabilities for the emergence of fixed-size components in random geometric graphs at the connectivity threshold, enhancing understanding of phase transitions in such networks.

Contribution

It provides exact asymptotic formulas for fixed-size component probabilities at the connectivity threshold in random geometric graphs.

Findings

Asymptotic expressions for fixed-size component probabilities.

Threshold behavior for connectivity in geometric graphs.

Enhanced understanding of phase transitions in network connectivity.

Abstract

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.