Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917622137749504 |
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| author | Cao, Shiping Qiu, Hua |
| author_facet | Cao, Shiping Qiu, Hua |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_17311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets Cao, Shiping Qiu, Hua Functional Analysis Metric Geometry Probability 28A80, 31E05 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. |
| title | Uniqueness and convergence of resistance forms on unconstrained Sierpinski carpets |
| topic | Functional Analysis Metric Geometry Probability 28A80, 31E05 |
| url | https://arxiv.org/abs/2403.17311 |