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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2506.17061 |
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| _version_ | 1866913904374841344 |
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| author | Thành, Lê Vǎn Tu, Nguyen Ngoc |
| author_facet | Thành, Lê Vǎn Tu, Nguyen Ngoc |
| contents | This paper establishes a non-uniform Berry--Esseen bound for non-normal approximation using Stein's method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathematique, 2024] to the context of non-normal approximation. As an application of the main result, we derive non-uniform Berry--Esseen bounds in non-central limit theorems for the magnetization in the Curie--Weiss model and the imitative monomer-dimer model. These extend some existing results in the literature, including Theorem 2.1 of Chatterjee and Shao [Ann. Appl. Probab., 2011] and Theorem 1 of Chen [J. Math. Physics, 2016]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model Thành, Lê Vǎn Tu, Nguyen Ngoc Probability 60F05 This paper establishes a non-uniform Berry--Esseen bound for non-normal approximation using Stein's method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathematique, 2024] to the context of non-normal approximation. As an application of the main result, we derive non-uniform Berry--Esseen bounds in non-central limit theorems for the magnetization in the Curie--Weiss model and the imitative monomer-dimer model. These extend some existing results in the literature, including Theorem 2.1 of Chatterjee and Shao [Ann. Appl. Probab., 2011] and Theorem 1 of Chen [J. Math. Physics, 2016]. |
| title | Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model |
| topic | Probability 60F05 |
| url | https://arxiv.org/abs/2506.17061 |