Random graph models provide a mathematical framework for capturing the structure and dynamics of complex networks by assigning probabilistic rules to vertex connections. Classical models such as the ...

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 ...

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 ...