Lukas Schoug: What is the Gaussian Free Field?

The Gaussian Free Field (GFF) is a model of a random surface, which is of great importance in probability theory, statistical mechanics and quantum field theory. The continuum version of the d-dimensional GFF can be viewed as a d-dimensional time generalization of the standard Brownian motion; in particular, a one-dimensional GFF is a Brownian bridge. Just as many random models have Brownian motion as their limit (under appropriate scaling), many random surface models have the GFF as their scaling limit.
The talk will be focused on the key properties of the two-dimensional GFF, but start with the discrete case for simplicity and some intuition.