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arXiv · 2609.04936

Homogenization of anisotropic diffusion on pre-Sierpi\'{n}ski carpets

Shiping Cao·Zhen-Qing Chen·Hua Qiu
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Abstract

We investigate the restoration of isotropy for anisotropic diffusions on pre-Sierpi\'nski carpets in the plane, a problem previously studied by Barlow, Hattori, Hattori and Watanabe \cite{BHHW} in which they obtained a weak homogenization property for the ratio of effective resistances of the anisotropic diffusions. We establish the weak convergence of these anisotropic diffusions to Brownian motion on the Sierpi\'nski carpet. As a consequence, we give an affirmative answer to the strong homogenization conjecture raised in \cite[p.3]{BHHW}.

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Shiping Cao, Zhen-Qing Chen, Hua Qiu. 2026-09-04. Homogenization of anisotropic diffusion on pre-Sierpi\'{n}ski carpets. https://arxiv.org/abs/2609.04936

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