The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method

Timothy M. Garoni; Aram Perez; Zongzheng Zhou

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arXiv · 2512.05340

The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method

Timothy M. Garoni·Aram Perez·Zongzheng Zhou

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Abstract

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.

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Timothy M. Garoni, Aram Perez, Zongzheng Zhou. 2025-12-05. The rate of convergence of the critical mean-field O(N) magnetization via multivariate nonnormal Stein's method. https://arxiv.org/abs/2512.05340

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