Acta Mathematica Vietnamica
Non-uniform Bounds for Non-normal Approximation via Stein’s Method with Applications to the Curie–Weiss Model and the Imitative Monomer-dimer Model
Lê Vǎn Thành
,
Nguyen Ngoc Tu
Abstract
This paper establishes a non-uniform Berry–Esseen bound for non-normal approximation using Stein’s method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathématique, 2024] to the context of non-normal approximation. As applications of the main result, we derive non-uniform Berry–Esseen bounds in non-central limit theorems for the magnetization in the Curie–Weiss model and the imitative monomer-dimer model. These extend some existing results in the literature, including Theorem 2.1 of Chatterjee and Shao [Ann. Appl. Probab., 2011] and Theorem 1 of Chen [J. Math. Physics, 2016].
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