First passage percolation with long-range correlations and applications to random Schrödinger operators

Abstract

We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on ${\mathbb{Z}}^d$, $d\ge 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla \varphi$ 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 function of RCMs with random killing measures.

54 pages

References in corpus (6)

• Random walks on supercritical percolation clusters
• Invariance principle for the random conductance model with unbounded conductances
• On the uniqueness of the infinite cluster of the vacant set of random interlacements
• Anomalous heat-kernel decay for random walk among bounded random conductances
• Upper bound on the disconnection time of discrete cylinders and random interlacements
• Finite range decompositions of Gaussian fields with applications to level-set percolation

Cited by in corpus (1)

• First passage percolation, local uniqueness for interlacements and capacity of random walk