Random graphs provide a mathematical framework for modelling networks in which connections between nodes occur with prescribed probabilities. Classical models such as the Erdős–Rényi graph establish ...

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 ...

Discrete structures are omnipresent in mathematics, computer science, statistical physics, optimisation and models of natural phenomena. For instance, complex random graphs serve as a model for social ...

Mathematicians proved in the early 1990s that randomly connecting routers produces the most efficient, resilient network topology. It took AWS roughly 30 years to turn that result into production ...

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 ...

As mathematical abstractions go, graphs are among the simplest. Scatter a bunch of points in a plane. Connect some of them with lines. That’s all a graph is. And yet they are incredibly powerful. They ...