Abstract
The Curie–Weiss model is a statistical physics model that describes the behavior of a system of particles with mutual interactions. In this paper, we apply Stein’s method to establish Berry–Esseen bounds for both normal and non-normal approximations of a broad types of Curie–Weiss model, incorporating a size-dependent inverse temperature. Our result encompasses the Blumer-Emery-Griffiths model as a particular instance, while surpassing the convergence rate of earlier findings by Eichelsbacher and Martschink (2014). By using Stein’s method, we provide a comprehensive analysis of the Curie–Weiss model, offering improved bounds on the rate of convergence.
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Funding
The first author’s research is partly support by the National Natural Science Foundation of China (Grant no. 12031005) and Shenzhen Outstanding Talents Training Fund, and the third author’s research is partially supported by the National Natural Science Foundation of China for Young Scientists of (Grant no. 12301183) and National Science Fund Program for Excellent Young Scientists (Overseas).
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Shao, QM., Zhang, M. & Zhang, ZS. Distributional Approximation for General Curie–Weiss Models with Size-dependent Inverse Temperatures. Sankhya A (2024). https://doi.org/10.1007/s13171-024-00351-z
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DOI: https://doi.org/10.1007/s13171-024-00351-z
Keywords
- Curie–Weiss model
- BEG model
- Rate of convergence
- Berry–Esseen bounds
- Normal approximation
- Non-normal approximation
- Stein’s method