Speaker: Martin Slowik (Mannheim)
Title: Scaling limit of the harmonic crystal with random conductances
Abstract: In this talk we consider discrete Gaussian free fields with ergodic random conductances on $\mathbb{Z}^d$, $d \geq 2$, subject to Dirichlet boundary conditions, where the conductances are possibly unbounded but satisfy an integrability condition. As our main result, we prove that, for almost all realisation of the environment, the rescaled field converges in law towards a continuous Gaussian field. We also present a scaling limit for both the covariances of the field and the variance of the Wick-renormalised square 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 Sebastian Andres and Anna-Lisa Sokol.
Speaker: Alessandra Cipriani (London)
