Invariance principle for the random conductance model in a degenerate ergodic environment

Abstract

We study a continuous time random walk, $X$, on ${\mathbb{Z}}^d$ in an environment of random conductances taking values in $(0,\infty )$. We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for $X$ under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser's iteration scheme.

Published at http://dx.doi.org/10.1214/14-AOP921 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org); in this version a minor technical gap in the proof of Theorem 3.7 has been closed

References in corpus (8)

• Random walks on supercritical percolation clusters
• Recent progress on the Random Conductance Model
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Invariance principle for the random conductance model with unbounded conductances
• Harnack inequalities on weighted graphs and some applications to the random conductance model
• Invariance Principle for the Random Conductance Model with dynamic bounded Conductances
• Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
• On the speed of Random Walks among Random Conductances

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• Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights
• Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters
• Hydrodynamics for the partial exclusion process in random environment
• Local Limit Theorems for the Random Conductance Model and Applications to the Ginzburg-Landau $\nabla \varphi$ Interface Model
• Green kernel asymptotics for two-dimensional random walks under random conductances
• Models of Gradient Type with Sub-Quadratic Actions
• Disconnection and entropic repulsion for the harmonic crystal with random conductances
• Lower Gaussian heat kernel bounds for the Random Conductance Model in a degenerate ergodic environment
• An invariance principle for one-dimensional random walks among dynamical random conductances
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• First passage percolation with long-range correlations and applications to random Schrödinger operators
• Eigenvalue fluctuations for lattice Anderson Hamiltonians: Unbounded potentials
• From quenched invariance principle to semigroup convergence with applications to exclusion processes
• Coupling between Brownian motion and random walks on the infinite percolation cluster
• Homogenization theory of random walks among deterministic conductances