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

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  • Dommers, Sander
  • Eichelsbacher, Peter

Abstract

We study the inhomogeneous Curie–Weiss model with external field, where the inhomogeneity 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.

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  • Dommers, Sander & Eichelsbacher, Peter, 2020. "Berry–Esseen bounds in the inhomogeneous Curie–Weiss model with external field," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 605-629.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:605-629
    DOI: 10.1016/j.spa.2019.02.007
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    1. Dommers, S. & Külske, C. & Schriever, P., 2017. "Continuous spin models on annealed generalized random graphs," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3719-3753.
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