Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets

Shiping Cao; Hua Qiu

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arXiv · 2403.17311

Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets

Shiping Cao·Hua Qiu

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Abstract

We prove the uniqueness of self-similar $D_4$-symmetric resistance forms on unconstrained Sierpinski carpets ($\mathcal{USC}$'s). Moreover, on a sequence of $\mathcal{USC}$'s $K_n, n\geq 1$ converging in Hausdorff metric, we show that the associated diffusion processes converge in distribution if and only if the geodesic metrics on $K_n, n\geq 1$ are equicontinuous with respect to the Euclidean metric.

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Shiping Cao, Hua Qiu. 2024-03-26. Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets. https://arxiv.org/abs/2403.17311

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