Network science studies complex systems by representing them as networks 1. This approach has proven quite fruitful because in many cases the network representation achieves a practically useful ...

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 ...

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 ...

For any α ∈ (0, 1) and any nα ≤ d ≤ n/2, we show that λ(G) ≤ Cα√d with probability at least 1− 1 n , where G is the uniform random undirected d-regular graph on n vertices, λ(G) denotes its second ...

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 ...