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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.10804 |
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| _version_ | 1866913692291956736 |
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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 in normal approximation for exchangeable pairs using Stein's method via a concentration inequality approach. The main theorem extends and improves several results in the literature, including those of Eichelsbacher and Löwe [Electron. J. Probab. 15, 2010, 962--988], and Eichelsbacher [arXiv:2404.07587, 2024]. The result is applied to obtain a non-uniform Berry--Esseen bound for the squared-length of the total spin in the mean-field classical $N$-vector models, and a non-uniform Berry--Esseen bound for Jack deformations of the character ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical $N$-vector models and Jack measures Thành, Lê Vǎn Tu, Nguyen Ngoc Probability 60F05 This paper establishes a non-uniform Berry--Esseen bound in normal approximation for exchangeable pairs using Stein's method via a concentration inequality approach. The main theorem extends and improves several results in the literature, including those of Eichelsbacher and Löwe [Electron. J. Probab. 15, 2010, 962--988], and Eichelsbacher [arXiv:2404.07587, 2024]. The result is applied to obtain a non-uniform Berry--Esseen bound for the squared-length of the total spin in the mean-field classical $N$-vector models, and a non-uniform Berry--Esseen bound for Jack deformations of the character ratio. |
| title | Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical $N$-vector models and Jack measures |
| topic | Probability 60F05 |
| url | https://arxiv.org/abs/2502.10804 |