times [@Avin] and a characterization of sharp thresholds for many monotone graph functions [@Goel]. This list is far from comprehensive, of course, and the random geometric graph is still an active research area.

The random geometric graph is also highly related to the random connection continuum percolation model. In that model, the vertex set is given by an (almost surely infinite) Poisson point process of fixed intensity on $\mathbb{R}^d$, and two points are connected with some probability that varies (and usually decreases) with their distance. In particular, the special case in which the radius of connection is deterministically fixed at 1 was the model that initiated the study of this kind of random geometry, in the seminal paper of Gilbert [@Gilbert]. The objects of interest in this model are the existence of an infinite connected component, as well as the behavior of the subset of $\mathbb{R}^d$ that is at distance at most 1 from one of the vertices of the graph (the so-called “Poisson blob”). Continuum percolation is treated in detail in a book-length monograph by Meester and Roy [@Meester], as well as in the more general work of Grimmett [@Grimmett].

Most of the work done on random geometric graphs 