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

Sander Dommers; Peter Eichelsbacher

doi:10.1016/j.spa.2019.02.007

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arXiv · 1809.10173

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

Sander Dommers·Peter Eichelsbacher

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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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Sander Dommers, Peter Eichelsbacher. 2018-09-26. Berry-Esseen bounds in the inhomogeneous Curie-Weiss model with external field. https://doi.org/10.1016/j.spa.2019.02.007

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