Scaling limit of the harmonic crystal with random conductances

In this talk we consider discrete Gaussian free fields with ergodic random conductances on ℤd, d ≥ 2, where the conductances are possibly unbounded but satisfy a moment condition. As our main result, we show that, for almost every realisation of the environment, the rescaled field converges in law towards a continuous Gaussian field. We also present a scaling limit for the covariances of the field. To obtain the latter, we establish a quenched local limit theorem for the Green’s function of the associated random walk among random conductances with Dirichlet boundary conditions. This talk is based on a joint work with Martin Slowik and Anna-Lisa Sokol.