Non-uniform bounds for non-normal approximation via Stein's method with applications to the Curie--Weiss model and the imitative monomer-dimer model

2025/06/20 by Thành, Lê Vǎn, Tu, Nguyen Ngoc
Computer Science · Economics, Econometrics and Finance · Mathematics · #60F05 #FOS: Mathematics #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2506.17061

openalex publication_date 2025/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Mathematique, 2024] to the context of non-normal approximation. As an application 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].

Citations

• Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical N-vector models and Jack measures
• Non-uniform Berry--Esseen bounds for Gaussian, Poisson and Rademacher processes
• Non-uniform Berry-Esseen bounds via Malliavin-Stein method
• Stein's method and a cubic mean-field model
• Moderate Deviation and Berry-Esseen Bounds in the p-Spin Curie-Weiss Model
• Non-uniform Berry-Esseen Bound by Unbounded Exchangeable Pair Approach
• On the error bound in the normal approximation for Jack measures
• Cramér-type moderate deviation of normal approximation for unbounded exchangeable pairs
• A cramér type moderate deviation theorem for the critical curie-weiss model
• Normal approximation under local dependence
• Stein's Method, Jack Measure, and the Metropolis Algorithm

Related

• Non-uniform Berry--Esseen bounds for exchangeable pairs with applications to the mean-field classical N-vector models and Jack measures
• Stein's method and a cubic mean-field model
• Non-uniform Berry-Esseen Bound by Unbounded Exchangeable Pair Approach
• Stein's method for dependent random variables occurring in Statistical Mechanics
• Stein's method via induction