Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical $N$-vector models and Jack measures

Lê Vǎn Thành; Nguyen Ngoc Tu

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arXiv · 2502.10804

Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical $N$-vector models and Jack measures

Lê Vǎn Thành·Nguyen Ngoc Tu

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Abstract

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 L\"{o}we [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.

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BibTeX RIS

Lê Vǎn Thành, Nguyen Ngoc Tu. 2025-02-15. Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical $N$-vector models and Jack measures. https://arxiv.org/abs/2502.10804

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