关于Talagrand积极性原理的一点注记
A note on Talagrand's positivity principle
摘要：
塔拉格兰德的正性原理指出，可以稍微扰动谢灵顿-柯克帕特里克模型中的哈密顿量，使得在扰动吉布斯测度下两个组态的重叠将变得典型的非负。在这篇笔记中，我们观察到，从SK模型的设置中抽象出来只会改进结果，而不需要对Talagrand的论点进行任何修改。在这个版本中，例如，积极性原则立即适用于设置Aizenman-Sims-Starr插值。此外，从SK模型中提取改进了Ghirlanda-Guerra恒等式中的条件，并因此导致确保重叠的正性所需的较小阶的扰动。
英文摘要：
Talagrand's positivity principle states that one can slightly perturb a Hamiltonian in the Sherrington-Kirkpatrick model in such a way that the overlap of two configurations under the perturbed Gibbs' measure will become typically nonnegative. In this note we observe that abstracting from the setting of the SK model only improves the result and does not require any modifications in Talagrand's argument. In this version, for example, positivity principle immediately applies to the setting of Aizenman-Sims-Starr interpolation. Also, abstracting from the SK model improves the conditions in the Ghirlanda-Guerra identities and as a consequence results in a perturbation of smaller order necessary to ensure positivity of the overlap.
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