Variational principles for random maps
Variational principles for random maps can be used to explain the appearance of limit shapes like the Aztec diamond for domino tilings.
As simulations suggest, variational principles should be valid for a wide class of models. Recently with Martin Tassy, we showed that the model of random graph homomorphisms to a regular tree satisfies a variational principle.
In this research area together with Andrew Krieger and Martin Tassy, we try to derive variational principles for other more complicated models.
Further reading: A variational principle for a non-integrable model, with Martin Tassy, arXiv:1610.08103.
Talk: Variational principles for discrete maps, Oberwolfach December 2016 and at the Southern California Probability Symposium.