New Frontiers in Random Geometric Graphs

Description and Aim

Aim: Discuss recent developments and future directions in random geometric graphs, continuum percolation and related models.

Description: Continuum percolation and random geometric graphs are closely related topics that started over half a century ago with the pioneering work of E.N. Gilbert. The objects of study are mathematical network models whereby a network is formed on random points in the plane (or some higher dimensional space) by connecting pairs of points according to some rule. The points are generated according to some random process such as the Poisson point process; and an example of a rule is to connect two points if their distance is less than some parameter r.

Such models have been the subject of sustained research effort over the past five decades. In the past decade or so, interest in the topic has heightened because of its relevance to real-world networks such as ad-hoc wireless networks. The topic is currently receiving considerable attention from the mathematics, computer science and engineering communities. As a result there is a growing body of impressive results that give a detailed description of several aspects of these models. Notwithstanding this, several challenging questions are left wide open and novel directions for research continue to be uncovered.

The main goals of the workshop are to facilitate the exchange of techniques, questions and ideas that will lead to a better understanding of continuum percolation/random geometric graphs; and to form new (international) collaborations for the exploration of this exciting research frontier.