Description
I will describe results for the macroscopic asymptotics in random lozenge tilings in a large class of two-dimensional domains, in particular identifying Gaussian free field fluctuations for the height field. The results rely on an analysis on a discrete Coulomb gas extending the one known for invariant ensembles of random matrices.
This is based on the joint work https://arxiv.org/abs/2601.16377 with Vadim Gorin and Alice Guionnet