Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

The Annals of Applied Probability, Vol. 28, No. 4 (August 2018), pp. 2003-2062 (60 pages) Given a graph, the popular “modularity” clustering method specifies a partition of the vertex set as the ...

Vertices arrive sequentially in space and are joined to existing vertices at random according to a preferential rule combining degree and spatial proximity. We investigate phase transitions in the ...

In an era driven by complex data, scientists are increasingly encountering information that doesn't lie neatly on flat, ...

This lecture course is devoted to the study of random geometrical objects and structures. Among the most prominent models are random polytopes, random tessellations, particle processes and random ...