Homogenization of non-divergence form operators in i.i.d. random environments
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914182874529792 |
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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 |