Berry-Esseen bounds in the inhomogeneous Curie-Weiss model with external field

Dommers, Sander; Eichelsbacher, Peter

Abstract

We study the inhomogeneous Curie-Weiss model with external field, where the inhomo-geneity is introduced by adding a positive weight to every vertex and letting the interaction strength between two vertices be proportional to the product of their weights. In this model, the sum of the spins obeys a central limit theorem outside the critical line. We derive a Berry-Esseen rate of convergence for this limit theorem using Stein's method for exchangeable pairs. For this, we, amongst others, need to generalize this method to a multidimensional setting with unbounded random variables.

Citation

Dommers, S., & Eichelsbacher, P. (in press). Berry-Esseen bounds in the inhomogeneous Curie-Weiss model with external field. Stochastic processes and their applications, https://doi.org/10.1016/j.spa.2019.02.007

• Journal Article Type: Article
• Acceptance Date: Feb 13, 2019
• Online Publication Date: Feb 22, 2019
• Deposit Date: Feb 13, 2019
• Publicly Available Date: Feb 22, 2019
• Journal: Stochastic processes and their applications
• Print ISSN: 0304-4149
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1016/j.spa.2019.02.007
• Keywords: Regeneration times; CLT rates of convergence; Random walks in random environments
• Public URL: https://hull-repository.worktribe.com/output/1299282
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0304414918305295