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INTERNATIONAL JOURNAL OF SCIENTIFIC DEVELOPMENT AND RESEARCH International Peer Reviewed & Refereed Journals, Open Access Journal ISSN Approved Journal No: 2455-2631 | Impact factor: 8.15 | ESTD Year: 2016 open access , Peer-reviewed, and Refereed Journals, Impact factor 8.15 |
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| Paper Title: | Error bounds in nonnormal approximation for the total magnetization in the general Curie-Weiss model |
| Authors Name: | Anh, Vo Thi Van , Khuyen, Nguyen Le Bao |
| Unique Id: | IJSDR2207052 |
| Published In: | Volume 7 Issue 7, July-2022 |
| Abstract: | The Curie-Weiss model is important in statistical mechanics and has been extensively discussed in the literature. The model not only displays a phase transition, with distinct behaviors at high and low temperature, but also serve as an illustration of various techniques and show how the probabilistic behavior is intimately related to the analytic properties of the thermodynamic potentials (free energy and pressure) of the model. For some history and an overview of first asymptotic results on the Curie-Weiss models, the reader is referred to Ellis and Newman (1978a, 1978b). Using the technique of exchangeable pair approach, Chatterjee and Shao (2011) and Eichelbacher and Löwe (2010) studied a kind of classical Curie-Weiss model. Shao and Zhang (2019) studied a general Curie-Weiss model and got the optimal convergence rate for Kolmogorov bound. In this paper, we establish the Wasserstein bound in nonnormal approximation for the total magnetization in the general Curie-Weiss model at the critical temperature. The proof is based on Stein’s method for exchangeable pairs. |
| Keywords: | Stein’s method, exchangeable pairs, general Curie-Weiss model |
| Cite Article: | "Error bounds in nonnormal approximation for the total magnetization in the general Curie-Weiss model", International Journal of Science & Engineering Development Research (www.ijsdr.org), ISSN:2455-2631, Vol.7, Issue 7, page no.380 - 382, July-2022, Available :http://www.ijsdr.org/papers/IJSDR2207052.pdf |
| Downloads: | 000337362 |
| Publication Details: | Published Paper ID: IJSDR2207052 Registration ID:200977 Published In: Volume 7 Issue 7, July-2022 DOI (Digital Object Identifier): http://doi.one/10.1729/Journal.31046 Page No: 380 - 382 Publisher: IJSDR | www.ijsdr.org ISSN Number: 2455-2631 |
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