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 ...

Transactions of the American Mathematical Society, Vol. 367, No. 4 (APRIL 2015), pp. 2509-2526 (18 pages) In a previous paper, we applied Alexandrov geometry methods to study infinite semiplanar ...

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 ...

This is a graduate topics course on learning in networks, focusing in particular on fundamental statistical and computational limits. Topics include the planted clique problem, community detection, ...