Quenched invariance principles for random walks on percolation clusters

Abstract

We prove the almost sure ('quenched') invariance principle for a random walker on an infinite Bernoulli percolation cluster in ${\mathbb{Z}}^d$ where $d$ is larger or equal than 2.

Different and more self-contained exposition of the main step of the proof. Paper can now be read without any previous knowledge on 2 scale convergence

References in corpus (2)

• Quenched invariance principle for simple random walk on percolation clusters
• Random walks on supercritical percolation clusters

Cited by in corpus (3)

• Quenched invariance principle for simple random walk on percolation clusters
• Isoperimetric inequalities and mixing time for a random walk on a random point process
• Note on the Heat-Kernel Decay for Random Walk among Random Conductances with Heavy Tail