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 ...

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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 ...

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 ...

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 = ...

Deep in the heart of Microsoft, Jennifer Chayes and Christian Borgs lead a who's who of mathematics and computer science. The goal? To explore anything they please Every weekday afternoon some 20 ...

Now that pandemic restrictions are easing up, people are getting together again. But it’s been a while, so if you and your friends need some help breaking the ice, here’s a mathematical party game you ...