Abstract
We study the large-volume asymptotics of the sum of power-weighted edge lengths in Poisson-based spatial random networks. In the regime α>d, we provide a set of sufficient conditions under which the upper large deviations asymptotics are characterized by a condensation phenomena, meaning that the excess is caused by a negligible portion of Poisson points. Moreover, the rate function can be expressed through a concrete optimization problem. This framework encompasses in particular directed, bidirected and undirected variants of the k-nearest neighbor graph, as well as suitable β-skeletons.
Type
Publication
Adv. App. Probab