Victor Falgas-Ravry: Small components in the k-nearest neighbour random geometric graph

The k-nearest neighbour random geometric graph model S_{n,k} is obtainedby scattering vertices inside a square S_n of area n according to a Poisson point process of intensity 1, and placing an (undirected) edge between each vertex and the k=k(n) points of the process closest to it.

In this talk I present some recent results about the size and distribution of small components in S_{n,k} for k below the connectivity threshold.