We consider an application of probabilistic coupling techniques which provides explicit estimates for comparison of local expectation values between label permutation invariant states, for instance, between certain microcanonical, canonical, and grand canonical ensemble expectations. A particular goal is to obtain good bounds for how such errors will decay with increasing system size. As explicit examples, we focus on two well-studied mean-field models: the discrete model of a paramagnet and the mean-field spherical model of a continuum field, both of which are related to the Curie–Weiss model. The proof is based on a construction of suitable probabilistic couplings between the relevant states, using Wasserstein fluctuation distance to control the difference between the expectations in the thermodynamic limit.

中文翻译：

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使用耦合技术估计两个格子平均场模型中的局部微正则平均值

我们考虑概率耦合技术的应用，该技术为标签置换不变状态之间的局部期望值的比较提供了明确的估计，例如，某些微正则、正则和大正则集合期望之间的比较。一个特定的目标是获得关于此类错误如何随着系统规模增加而衰减的良好界限。作为明确的例子，我们关注两个经过充分研究的平均场模型：顺磁体的离散模型和连续场的平均场球面模型，两者都与居里-魏斯模型有关。该证明基于在相关状态之间构建合适的概率耦合，使用 Wasserstein 波动距离来控制热力学极限中期望值之间的差异。