论文标题
使用耦合技术在两个晶格平均场模型中估算局部微型人体平均值
Estimation of local microcanonical averages in two lattice mean-field models using coupling techniques
论文作者
论文摘要
我们考虑了概率耦合技术的应用，该技术提供了明确的估计值，以比较标签置换不变状态之间的局部期望值，例如，在某些微型典型，规范和大规范的集合期望之间。一个特定的目标是获得良好的界限，以使这些错误如何随着系统大小的增加而衰减。作为明确的示例，我们专注于两个经过良好研究的均值模型：paramagnet的离散模型和连续场的平均场球形模型，这两者都与居里 - 韦斯式模型有关。该证明是基于使用瓦斯汀波动距离来控制热力学极限中期望之间的差异的相关状态之间合适概率耦合的构造。
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.
