Abstract: We know that large random combinatorial structures (e.g., graphs, tilings, Ising configurations) with given parameters tend to look alike.  But what do they look like?

In the case of permutations, we can in some cases answer this question with the help of limit structures called “permutons,” together with a variational principle. We’ll present some examples, showing very nice apparent behavior and uncovering some intriguing contrasts with the case of graphs and their limit structures (graphons).

This is joint work with Rick Kenyon, Dan Kral’ and Charles Radin.