Inhomogeneous Long-Range Percolation for Real-Life Network Modeling

Abstract

The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice ${\mathbb{Z}}^d$, $d\ge 1$, is a particular attractive example of a random graph model because it fulfills several stylized facts of real-life networks. For this model various geometric properties such as the percolation behavior, the degree distribution and graph distances have been analyzed. In the present paper we complement the picture about graph distances. Moreover, we prove continuity of the percolation probability in the phase transition point.

19 pages, new version. Substantially modified version

References in corpus (3)

• On the scaling of the chemical distance in long-range percolation models
• A lower bound for the chemical distance in sparse long-range percolation models
• Distances in critical long range percolation