Kurt Johansson: Edge fluctuations of limit shapes

I will survey results on the fluctuations of the boundaries between regions with different phases in some random tiling or dimer models. These fluctuations are of a universal nature and the same type of limit laws appear also in other contexts, in particular in local random growth models, directed polymers and random matrix theory. Behind the fact that certain models can be analyzed in detail is the fact that the tiles or dimers form determinantal point processes.