Invariance Principle for the Random Conductance Model with dynamic bounded Conductances

Abstract

We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X, and obtain Green's functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.

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• Local Limit Theorems for the Random Conductance Model and Applications to the Ginzburg-Landau $\nabla \varphi$ Interface Model
• A quenched local limit theorem for stochastic flows
• Green kernel asymptotics for two-dimensional random walks under random conductances
• Symmetric simple exclusion process in dynamic environment: hydrodynamics
• An invariance principle for one-dimensional random walks among dynamical random conductances
• Random partitions under the Plancherel-Hurwitz measure, high genus Hurwitz numbers and maps
• The Discrete Gaussian model, II. Infinite-volume scaling limit at high temperature
• The Discrete Gaussian model, I. Renormalisation group flow at high temperature
• Homogenization theory of random walks among deterministic conductances