AN ELLIPTIC HARNACK INEQUALITY FOR DIFFERENCE EQUATIONS WITH RANDOM BALANCED COEFFICIENTS

Noam Berger, Moran Cohen, Jean Dominique Deuschel, Xiaoqin Guo

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We prove an elliptic Harnack inequality at large scale on the lattice Zd for nonnegative solutions of a difference equation with balanced i.i.d. coefficients which are not necessarily elliptic.We also identify the optimal constant in the Harnack inequality. Our proof relies on a quantitative homogenization result of the corresponding invariance principle to Brownian motion and on percolation estimates. As a corollary of our main theorem, we derive an almost optimal Hölder estimate.

Original languageEnglish
Pages (from-to)835-873
Number of pages39
JournalAnnals of Probability
Volume50
Issue number3
DOIs
StatePublished - May 2022

Keywords

  • Balanced environment
  • Elliptic harnack inequality
  • Non-ellipticity
  • Nondivergence form operators
  • Percolation
  • Random walks in random environments

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