Advances in Applied Probability, Vol. 50, No. 1 (2018), pp. 272-301 (30 pages) We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the ...

Journal of Applied Probability, Vol. 47, No. 3 (SEPTEMBER 2010), pp. 826-840 (15 pages) A random intersection graph G(n, m, p) is defined on a set 𝓥 of n vertices. There is an auxiliary set 𝓦 ...

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 ...

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 ...

Expanders graphs are sparse but well-connected. These seemingly contrasting properties have led to many applications in theoretical computer science, from complexity ...