On the random G equation with nonzero divergence

TL;DR

This paper establishes a quantitative homogenization rate for the G equation in a random environment with nonzero divergence, providing explicit bounds based on the environment's Lipschitz norm.

Contribution

It introduces a novel homogenization rate for the G equation with nonzero divergence in random settings, extending previous work to more general environments.

Findings

Quantitative homogenization rate derived

Explicit dependence on environment's Lipschitz norm

Bounds on waiting time for metric problem provided

Abstract

We prove a quantitative rate of homogenization for the G equation in a random setting with finite range of dependence and nonzero divergence, with explicit dependence of the constants on the Lipschitz norm of the environment. Inspired by work of Burago, Ivanov, and Novikov, the proof uses explicit bounds on the waiting time for the associated metric problem.