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 ...

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 ...

This is a preview. Log in through your library . Abstract Given two independent Poisson point processes Φ (1) , Φ (2) in ${\mathrm{\mathbb{R}}}^{\mathrm{d}}$ , the AB Poisson Boolean model is the ...

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 ...

Six years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets when they stumbled into a surreal world. Ling realized that the ...