The Martingale Method for Mean-Field Disordered Systems at High Temperature
The Martingale Method for Mean-Field Disordered Systems at High Temperature
复制标题
高温平均场无序系统的鞅法
DOI：
10.1007/978-1-4612-4102-7_2
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
F. Comets
中科院分区：
文献类型：
--
作者：
F. Comets
本文综述了研究高温平均场无序系统的鞅方法，包括Sherrington-Kirkpatrick模型、Hopfield模型和更一般的联想记忆模型。我们用布朗运动描述了配分函数的对数正态极限，并给出了压力自平均的另一个证明。在谢灵顿-柯克帕特里克的情况下，我们表明，两个独立的配置的产品的法律是在非常高的温度接近一致的，但这并不坚持在整个高温区。
We review some martingale techniques for the study of meanfield disordered systems at high temperature, including the Sherrington-Kirkpatrick model, the Hopfield model, and more general associative memory models. We describe the log-normal limit of the partition function in term of a Brownian motion, and we give another proof of self-averaging for pressure. In the Sherrington-Kirkpatrick case we show that the law of the product of two independent configurations is close to uniform at very high temperature, but this does not persist in the whole high-temperature region.