标题： 退化随机导电率下的离散高斯自由场的尺度极限 显示英文标题

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

摘要： 我们考虑在$\mathbb{Z}^{d}$,$d \geq 2$的随机子图类上的具有遍历随机导电率的离散高斯自由场，包括独立同分布的超临界渗流簇，其中导电率可能是无界的，但满足矩条件。 作为主要结果，我们证明对于环境的几乎每个实现，归一化的场在分布上收敛于连续高斯自由场。 我们还给出了场协方差的尺度极限。 为了得到后者，我们建立了在具有狄利克雷边界条件的随机导电率下的相关随机游走的格林函数的淬火局部极限定理。 显示英文摘要

摘要： We consider discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of $\mathbb{Z}^{d}$, $d \geq 2$, 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.