Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866908933819465728 |
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| author | Sasaya, Kôhei |
| author_facet | Sasaya, Kôhei |
| contents | The spectral dimension $d_s$ of a weighted graph is an exponent associated with the asymptotic behavior of the random walk on the graph. The Ahlfors regular conformal dimension $\dim_\mathrm{ARC}$ of the graph distance is a quasisymmetric invariant, where quasisymmetry is a well-studied property of homeomorphisms between metric spaces. In this paper, we give a typical example of a fractal-like graph with $d_s<\dim_\mathrm{ARC}<2$ and prove a sufficient condition for $\dim_\mathrm{ARC}\le d_s<2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_00851 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs Sasaya, Kôhei Probability 60J10 (Primary), 30L10 (Secondary) The spectral dimension $d_s$ of a weighted graph is an exponent associated with the asymptotic behavior of the random walk on the graph. The Ahlfors regular conformal dimension $\dim_\mathrm{ARC}$ of the graph distance is a quasisymmetric invariant, where quasisymmetry is a well-studied property of homeomorphisms between metric spaces. In this paper, we give a typical example of a fractal-like graph with $d_s<\dim_\mathrm{ARC}<2$ and prove a sufficient condition for $\dim_\mathrm{ARC}\le d_s<2.$ |
| title | Some relation between spectral dimension and Ahlfors regular conformal dimension on infinite graphs |
| topic | Probability 60J10 (Primary), 30L10 (Secondary) |
| url | https://arxiv.org/abs/2109.00851 |