关于Curie-Weiss随机场模型中重叠浓度的研究
On overlap concentration in the Curie-Weiss Random Field model
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中文总结 AI 辅助
该研究证明了在特定条件下Curie-Weiss随机场模型中两个独立副本的重叠具有次高斯尾部，通过Laplace近似和速率函数分析实现。
中文摘要 AI 辅助
我们证明了，当逆温度 $ \eta < 1$ 且随机场服从高斯分布，使得Curie-Weiss随机场（CWRF）模型的期望磁化强度在热力学极限下等于其期望重叠时，从该模型Gibbs测度中抽取的两个独立副本的重叠具有次高斯尾部。为证明这一点，我们通过针对某个随机速率函数的严格Laplace近似证明了有限矩浓度，并利用对相关速率函数的精细分析，将其“自举”为平方重叠偏差的矩生成函数的均匀界。
英文摘要
We show that the overlaps of two independent replicas drawn from the Gibbs measure of the Curie--Weiss model with random field (CWRF) exhibit sub-Gaussian tails when the inverse temperature $ β< 1$ and the random field is drawn from a Gaussian distribution that makes the expected magnetization of the CWRF equal to its expected overlap in the thermodynamic limit. To show this, we prove finite-moment concentration via a rigorous Laplace approximation for a certain random rate function, and ``bootstrap'' it to a uniform bound for the moment-generating function of the squared overlap deviations using a sharp analysis of the associated rate function.
发表机构
- Johns Hopkins University（约翰斯·霍普金斯大学）
- Colorado State University（科罗拉多州立大学）
- Chipletics Inc（Chipletics公司）
机构由 AI 辅助整理，请以论文原文为准。
