Scaling limit of the discrete Gaussian free field with degenerate random conductances

2025/08/24 by Andres, Sebastian, Slowik, Martin, Sokol, Anna-Lisa · 2 citations
#39A12 #60J35 #60J45 #60K37 #82C41 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2508.17369

Abstract

We consider discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of ℤ^d, d ≥ 2, including i.i.d. supercritical percolation clusters, where the conductances are possibly unbounded but satisfy a moment condition. As our main result, we show that, for almost every realization of the environment, the rescaled field converges in law towards a continuum Gaussian free 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.

Citations

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Cited by

• Hard wall repulsion for the discrete Gaussian free field in random environment on ℤ^d, d≥ 3
• Solidification estimates for random walks on supercritical percolation clusters

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• Invariance principles for operator-scaling Gaussian random fields