Random interfaces and random matrices

One-dimensional random interfaces occur for example in random growth models and random tiling models.

In some models their statistical properties turn out to be related to random matrix statistics. I will concentrate on random tiling or dimer models like the Aztec diamond and discuss the statistics of the tiles/dimers. The models can also be interpreted as certain random surfaces. Associated with these models are random point processes that are so called determinantal point processes. I will discuss these processes and their scaling limits which are expected to be universal scaling limits in the sense that they should be natural scaling limits in various models. The talk will give an overview of some developments in this area aimed at a general audience.