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 ...

The so-called differential equation method in probabilistic combinatorics presented by Patrick Bennett, Ph.D., Department of Mathematics, Western Michigan University Abstract: Differential equations ...

We study the uniform random graph Cn with n vertices drawn from a subcriticai class of connected graphs. Our main result is that the rescaled graph On ${C_n}/\sqrt n $ converges to the Brownian ...

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 ...

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 ...

Abstract: Given a (monotone) graph property P and a random graph G(n,m) with n vertices and m edges, typically, there is a value m(n) such that P holds (does not hold) with probability approaching 1 ...

Back in the hazy olden days of the pre-2000s, navigating between two locations generally required someone to whip out a paper map and painstakingly figure out the most optimal route between those ...