Abstract: Statistical mechanics deals with measures in high dimensions.
Basically there are only three situations where we can deal effectively with such measures: when the measure is a product measure;
when it is Gaussian; or when it is
determinantal. The third case is the least familiar. We discuss a model of tilings in the plane with
convex polygonal tiles, related to a determinantal measure. One main result, roughly stated, is ``choose your favorite shape for each tile
(up to scale, and subject to the constraint that adjacent
tiles have their common edges in the same direction), then there is a tiling with those shapes".