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 ...

Quantum graphs—networks composed of vertices connected by edges on which quantum wave dynamics are defined—have emerged as a versatile model for exploring the interplay between geometry, topology, and ...

This is a preview. Log in through your library . Abstract In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a ...

This is a preview. Log in through your library . Abstract We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition ...