We investigate the rank of the adjacency matrix of large diluted random graphs: for a sequence of graphs (G n ) n≥0 converging locally to a Galton—Watson tree T (GWT), we provide an explicit formula ...

We consider a random field {Xij, i, j = 1, ⋯, n} where the random variables Xij takes on values 1 or 0. The collection {Xij} can be viewed as a random graph with nodes {1, ⋯, n} by interpreting Xij = ...

Graph limit theory provides a rigorous framework for analysing sequences of large graphs by representing them as continuous objects known as graphons – symmetric measurable functions on the unit ...

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 ...

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 ...