Quantitative stochastic homogenization of the G equation

TL;DR

This paper establishes a quantitative rate of homogenization for the G equation in random environments with finite dependence, advancing understanding of stochastic homogenization through percolation theory techniques.

Contribution

It provides the first quantitative homogenization rate for the G equation in finite-range dependent random environments, building on and extending previous qualitative results.

Findings

Quantitative homogenization rate established

Utilizes percolation theory methods

Extends qualitative results to quantitative context

Abstract

We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps a result of Cardaliaguet and Souganidis, who proved qualitative homogenization in a more general ergodic environment.