학술논문
Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets
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Working Paper
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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.
Comment: 33 pages, 4 figures. This is the second part of the old version arXiv:2104.01529
Comment: 33 pages, 4 figures. This is the second part of the old version arXiv:2104.01529