Homogenization of non-divergence form operators in i.i.d. random environments

Fuente: arXiv
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Auteurs principaux: Guo, Xiaoqin, Sprekeler, Timo, Tran, Hung V.
Format: Preprint
Publié: 2025
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author Guo, Xiaoqin
Sprekeler, Timo
Tran, Hung V.
author_facet Guo, Xiaoqin
Sprekeler, Timo
Tran, Hung V.
contents We study random walks in a balanced, i.i.d. random environment in $\mathbb Z^d$ for $d\geq 3$. We establish improved convergence rates for the homogenization of the Dirichlet problem associated with the corresponding non-divergence form difference operators, surpassing the $O(R^{-1})$ rate, which is expected to be optimal for environments with a finite range of dependence. In particular, the improved rates are $O(R^{-3/2})$ when $d=3$, and $O(R^{-2}\log R)$ when $d\geq 4$.
format Preprint
id arxiv_https___arxiv_org_abs_2512_04410
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Homogenization of non-divergence form operators in i.i.d. random environments
Guo, Xiaoqin
Sprekeler, Timo
Tran, Hung V.
Probability
Analysis of PDEs
35J15, 35J25, 60G50, 60K37, 74Q20, 76M50
We study random walks in a balanced, i.i.d. random environment in $\mathbb Z^d$ for $d\geq 3$. We establish improved convergence rates for the homogenization of the Dirichlet problem associated with the corresponding non-divergence form difference operators, surpassing the $O(R^{-1})$ rate, which is expected to be optimal for environments with a finite range of dependence. In particular, the improved rates are $O(R^{-3/2})$ when $d=3$, and $O(R^{-2}\log R)$ when $d\geq 4$.
title Homogenization of non-divergence form operators in i.i.d. random environments
topic Probability
Analysis of PDEs
35J15, 35J25, 60G50, 60K37, 74Q20, 76M50
url https://arxiv.org/abs/2512.04410