Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914707772801024 |
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| author | Andres, Sebastian Croydon, David A. Kumagai, Takashi |
| author_facet | Andres, Sebastian Croydon, David A. Kumagai, Takashi |
| contents | We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using standard techniques, with key inputs coming from a careful analysis of the volume growth of the invariant measure of the process under study. As for the quantitative homogenization results, these include both quenched and annealed Berry-Esseen-type theorems, as well as a quantitative quenched local limit theorem. Whilst the model we study here is a particularly simple example of a random walk in a random environment, we believe the roadmap we provide for establishing the latter result in particular will be useful for deriving quantitative local limit theorems in other, more challenging, settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_11115 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model Andres, Sebastian Croydon, David A. Kumagai, Takashi Probability Analysis of PDEs 60K37, 60F17, 82C41, 82B43 We present on-diagonal heat kernel estimates and quantitative homogenization statements for the one-dimensional Bouchaud trap model. The heat kernel estimates are obtained using standard techniques, with key inputs coming from a careful analysis of the volume growth of the invariant measure of the process under study. As for the quantitative homogenization results, these include both quenched and annealed Berry-Esseen-type theorems, as well as a quantitative quenched local limit theorem. Whilst the model we study here is a particularly simple example of a random walk in a random environment, we believe the roadmap we provide for establishing the latter result in particular will be useful for deriving quantitative local limit theorems in other, more challenging, settings. |
| title | Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model |
| topic | Probability Analysis of PDEs 60K37, 60F17, 82C41, 82B43 |
| url | https://arxiv.org/abs/2310.11115 |