Stein’s Method and a Cubic Mean-Field Model

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Peter Eichelsbacher
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引用次数: 0

Abstract

In this paper, we study a mean-field spin model with three- and two-body interactions. In a recent paper (Ann Henri Poincaré, 2024) by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point. The authors proved a central limit theorem for the suitably rescaled magnetization. The aim of our paper is presenting a prove of a central limit theorem for the rescaled magnetization applying the exchangeable pair approach due to Stein. Moreover we prove (non-uniform) Berry–Esseen bounds, a concentration inequality, Cramér-type moderate deviations and a moderate deviations principle for the suitably rescaled magnetization. Interestingly we analyze Berry–Esseen bounds in case the model-parameters \((K_n,J_n)\) converge to the critical point (0, 1) on lines with different slopes and with a certain speed, and obtain new limiting distributions and thresholds for the speed of convergence.

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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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