AI 中文总结
本文针对零场Sherrington-Kirkpatrick模型，在逆温度为一时定量比较不同失序分布，证明在临界重叠极限下将高斯耦合替换为有界对称分布仅引起受控误差，并推广至Wasserstein拓扑下的收敛。
AI 中文摘要
我们在逆温度为一的零场Sherrington-Kirkpatrick模型中给出了定量的失序比较。对于任意固定数量的副本，将高斯耦合替换为来自有界对称方差为一分布的独立耦合，会使有界副本期望至多改变一个常数乘以高斯重叠二阶矩再加上N^{-1}。对于非负可观测量的乘法比较控制了尾部。证明使用了Talagrand的正可观测量估计和Yu-Ting Chen的四阶副本消去。假设Du和Huang所述的临界高斯重叠极限成立，我们在迭代Wasserstein-2拓扑下对随机淬火重叠测度获得相同的极限。此传递不需要单独的矩假设。他们额外的指数矩界给出了在每一有限Wasserstein距离下重标度自旋玻璃磁化率的收敛。耦合类包括公平符号、均匀失序以及以任何固定正密度稀疏化的符号。
英文摘要
We give a quantitative disorder comparison for the zero-field Sherrington--Kirkpatrick model at inverse temperature one. For any fixed number of replicas, replacing Gaussian couplings by independent couplings from a bounded symmetric variance-one law changes a bounded replica expectation by at most a constant times the Gaussian overlap second moment plus $N^{-1}$. A multiplicative comparison for nonnegative observables controls the tails. The proof uses Talagrand's positive-observable estimates and Yu-Ting Chen's fourth-order replica cancellation. Assuming the Gaussian critical overlap limit stated by Du and Huang, we obtain the same limit for the random quenched overlap measure in the iterated Wasserstein-2 topology. No separate moment assumption is needed for this transfer. Their additional exponential moment bound gives convergence of the rescaled spin-glass susceptibility in every finite Wasserstein distance. The coupling class includes fair signs, uniform disorder, and signs thinned at any fixed positive density.
Comments8 pages, 1 figure
