Aging and sub-aging for Bouchaud trap models on resistance metric spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910739844825088 |
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| author | Noda, Ryoichiro |
| author_facet | Noda, Ryoichiro |
| contents | In this paper, we prove that if a sequence of electrical networks converges in the local Gromov-Hausdorff topology and satisfies a non-explosion condition, then the associated Bouchaud trap models (BTMs) also converge and exhibit aging. Moreover, when local structures of electrical networks converge, we prove sub-aging. Our results are applicable to a wide class of low-dimensional graphs, including the two-dimensional Sierpiński gasket, critical Galton-Watson trees, and the critical Erdős-Rényi random graph. The proof consists of two main steps: Polish metrization of the vague-and-point-process topology and showing the precompactness of transition densities of BTMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08236 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Aging and sub-aging for Bouchaud trap models on resistance metric spaces Noda, Ryoichiro Probability 60K37 (Primary) 28A33, 60J27, 60J35, 82B41, 82D30 (Secondary) In this paper, we prove that if a sequence of electrical networks converges in the local Gromov-Hausdorff topology and satisfies a non-explosion condition, then the associated Bouchaud trap models (BTMs) also converge and exhibit aging. Moreover, when local structures of electrical networks converge, we prove sub-aging. Our results are applicable to a wide class of low-dimensional graphs, including the two-dimensional Sierpiński gasket, critical Galton-Watson trees, and the critical Erdős-Rényi random graph. The proof consists of two main steps: Polish metrization of the vague-and-point-process topology and showing the precompactness of transition densities of BTMs. |
| title | Aging and sub-aging for Bouchaud trap models on resistance metric spaces |
| topic | Probability 60K37 (Primary) 28A33, 60J27, 60J35, 82B41, 82D30 (Secondary) |
| url | https://arxiv.org/abs/2412.08236 |