An elliptic Harnack inequality for random walk in balanced environments

Abstract

We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.

arXiv comment37 pages, 3 figures

References in corpus (2)

• Random walks on supercritical percolation clusters
• Quenched invariance principle for random walks in balanced random environment

Cited by in corpus (3)

• A parabolic Harnack principle for balanced difference equations in random environments
• Quantitative homogenization in a balanced random environment
• Quenched invariance principle for long range random walks in balanced random environments