Quenched invariance principles for random walks with random conductances

Abstract

We prove an almost sure invariance principle for a random walker among i.i.d. conductances in ${\mathbb{Z}}^d$, $d\ge 2$. We assume conductances are bounded from above but we dot require they are bounded from below.

Revised version

References in corpus (2)

• Random walks on supercritical percolation clusters
• Anomalous heat-kernel decay for random walk among bounded random conductances

Cited by in corpus (61)

• Recent progress on the Random Conductance Model
• Invariance principle for the random conductance model with unbounded conductances
• Anomalous heat-kernel decay for random walk among bounded random conductances
• Elliptic regularity and quantitative homogenization on percolation clusters
• Invariance principle for the random conductance model in a degenerate ergodic environment
• Quenched invariance principle for random walks in balanced random environment
• Scaling limit for a class of gradient fields with nonconvex potentials
• Limit theory for random walks in degenerate time-dependent random environments
• Random Dirichlet environment viewed from the particle in dimension $d\ge 3$
• Convergence to a Gaussian by narrowing of central peak in Brownian yet non-Gaussian diffusion in disordered environments
• Knudsen gas in a finite random tube: transport diffusion and first passage properties
• Quenched invariance principle for the Knudsen stochastic billiard in a random tube
• Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights
• Invariance Principle for the Random Conductance Model with dynamic bounded Conductances
• Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models
• Quenched invariance principles for random walks and elliptic diffusions in random media with boundary
• Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters
• Hydrodynamics for the partial exclusion process in random environment
• Isoperimetric inequalities and mixing time for a random walk on a random point process
• The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
• Invariance principle for Mott variable range hopping and other walks on point processes
• Green kernel asymptotics for two-dimensional random walks under random conductances
• Hydrodynamic limit of gradient exclusion processes with conductances on $\bb Z^d$
• Optimal corrector estimates on percolation clusters
• Geodesics of Random Riemannian Metrics
• Random Conductance Models with Stable-like Jumps: Quenched Invariance Principle
• Quantitative version of the Kipnis-Varadhan theorem and Monte Carlo approximation of homogenized coefficients
• Random walks in random environments without ellipticity
• Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters
• Random walks and exclusion processes among random conductances on random infinite clusters: homogenization and hydrodynamic limit
• The random conductance model with Cauchy tails
• Hydrodynamic limit of symmetric exclusion processes in inhomogeneous media
• Entropic repulsion of Gaussian free field on high-dimensional Sierpinski carpet graphs
• Quenched Invariance Principle for a class of random conductance models with long-range jumps
• Trapping in the random conductance model
• A quantitative central limit theorem for the random walk among random conductances
• Annealed invariance principle for random walks on random graphs generated by point processes in ${\mathbb{R}}^d$
• Quenched invariance principle for simple random walk on discrete point processes
• Random walks with unbounded jumps among random conductances I: Uniform quenched CLT
• From the Sinai's walk to the Brox diffusion using bilinear forms
• Hydrodynamic limit of zero range processes among random conductances on the supercritical percolation cluster
• Diffusivity and Ballistic Behavior of Random Walk in Random Environment
• A conditional quenched CLT for random walks among random conductances on ${\mathbb{Z}}^d$
• On the speed of Random Walks among Random Conductances
• Note on the Heat-Kernel Decay for Random Walk among Random Conductances with Heavy Tail
• A Sobolev inequality and the individual invariance principle for diffusions in a periodic potential
• Large deviations for the local times of a random walk among random conductances in a growing box
• Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities
• Recurrence or transience of random walks on random graphs generated by point processes in ${\mathbb{R}}^d$
• Geodesics of Random Riemannian Metrics: Supplementary Material
• Decay of semigroup for an infinite interacting particle system on continuum configuration spaces
• Discrete Fractal Dimensions of the Ranges of Random Walks in ${\mathbb{Z}}^d$ Associate with Random Conductances
• A quantitative central limit theorem for the effective conductance on the discrete torus
• Conditional and uniform quenched CLTs for one-dimensional random walks among random conductances
• Standard Spectral Dimension for the Polynomial Lower Tail Random Conductances model
• Quenched invariance principle for a long-range random walk with unbounded conductances
• Scaling limits for symmetric Ito-Levy processes in random medium
• Heat-kernel estimates for random walk among random conductances with heavy tail
• Variance limite d'une marche aléatoire réversible en milieu aléatoire sur Z (Limit of the Variance of a Reversible Random Walk in Random Medium on Z)
• Functional CLT for random walk among bounded random conductances
• Homogenization theory of random walks among deterministic conductances