The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918233561366528 |
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| author | Garoni, Timothy M. Perez, Aram Zhou, Zongzheng |
| author_facet | Garoni, Timothy M. Perez, Aram Zhou, Zongzheng |
| contents | We study the distribution of the magnetization of the critical mean-field O(N) model with N > 1. Specifically, we bound the Wasserstein distance between the finite-volume and limiting distributions, in terms of the number of spins. To achieve this, we extend a recent multivariate nonnormal approximation theorem. This generalizes known results for the Curie-Weiss magnetization to the multivariate O(N) setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method Garoni, Timothy M. Perez, Aram Zhou, Zongzheng Probability Mathematical Physics We study the distribution of the magnetization of the critical mean-field O(N) model with N > 1. Specifically, we bound the Wasserstein distance between the finite-volume and limiting distributions, in terms of the number of spins. To achieve this, we extend a recent multivariate nonnormal approximation theorem. This generalizes known results for the Curie-Weiss magnetization to the multivariate O(N) setting. |
| title | The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2512.05340 |