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

Sander Dommers and Peter Eichelsbacher

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 605-629

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.

Date: 2020
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DOI: 10.1016/j.spa.2019.02.007

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