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

Dommers, Sander; Eichelsbacher, Peter

Authors

Sander Dommers

Peter Eichelsbacher



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 Oct 27, 2022
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

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Copyright Statement
© 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/







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