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 ...

In this paper we investigate first passage percolation on an inhomogeneous random graph model introduced by Bollobás et al. (2007). Each vertex in the graph has a type from a type space, and edge ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...