Abstract
We consider discrete non-divergence form difference operators in a random environment and the corresponding process – the random walk in a balanced random environment in with a finite range of dependence. We first quantify the ergodicity of the environment from the point of view of the particle. As a consequence, we quantify the quenched central limit theorem of the random walk with an algebraic rate. Furthermore, we prove an algebraic rate of convergence for the homogenization of the Dirichlet problems for both elliptic and parabolic non-divergence form difference operators.
Funding Statement
XG is supported by Simons Foundation’s Collaboration Grant for Mathematicians # 852943. JP was partially supported by NSA grants H98230-15-1-0049 and H98230-16-1-0318. HT is supported in part by NSF grant DMS-1664424.
Acknowledgments
We thank two anonymous referees whose comments improve the presentation of our article. We thank Scott Armstrong and Charlie Smart for letting us know their new version [6] of [5] on arXiv. XG did the main part of his work while at the University of Wisconsin Madison. He thanks Professors Timo Sepäläinen and other colleagues at the UW for their hospitality and the supportive environment they created.
Citation
Xiaoqin Guo. Jonathon Peterson. Hung V. Tran. "Quantitative homogenization in a balanced random environment." Electron. J. Probab. 27 1 - 31, 2022. https://doi.org/10.1214/22-EJP851
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