FIRST PASSAGE PERCOLATION WITH LONG-RANGE CORRELATIONS AND APPLICATIONS TO RANDOM SCHRÖDINGER OPERATORS

We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on Zd, d >= 2, including discrete Gaussian free fields, Ginzburg-Landau backward difference phi interface models or random interlacements as prominent examples. We show that the associated time constant is positive, the FPP distance is comparable to the Euclidean distance, and we obtain a shape theorem. We also present two applications for random conductance models (RCM) with possibly unbounded and strongly correlated conductances. Namely, we obtain a Gaussian heat kernel upper bound for RCMs with a general class of speed measures, and an exponential decay estimate for the Green's function of RCMs with random killing measures.