Spin Glasses: A New Direction for Probability Theory

在研究自旋玻璃的平均场模型(如著名的Sherrington Kirkpatrick模型)时，许多物理学家“发现”(或更准确地说，猜测)了概率论中的一些全新现象，即在相关随机变量的大族的近极值之间存在复杂的结构。本研究的主要目的是通过对主要模型的研究，为他们的猜想提供严格的数学基础。两个主要目标是对主要模型的整个高温区的控制，以及对最简单模型的低温阶段的完整描述。概率论的中心主题之一是在大量随机事件中出现一种秩序。这是由主要的经典定理表示的，从大数定律开始。这些经典结果与事件相互独立，即不相互影响的情况有关。这样的假设在实践中是不现实的。我们调查了在随机事件的大型集合中出现的新类型的集体行为，其中每个事件都可以并将影响所有其他事件。

9988480Talagrand While studying mean field models for spin glasses (such as the famous Sherrington Kirkpatrick model) a number of physicists "discovered" (or more accurately, conjectured) some completely new phenomenon of probability theory, namely the existence of intricate structures among the near extreme values of large families of correlated random variables. The main goal of this research is, through the study of the main models, to provide mathematically rigorous foundations for their conjectures. Two main objectives are the control of the entire high temperature region for the main models, and a complete description of the low temperature phase of the simplest models. One of the central themes of probability theory is the emergence of a kind of order out of large number of random events. This is expressed by the main classical theorems, starting with the law of large numbers. These classical result relate to situations where the events are independent, that is do not influence each other. Such an assumption is unrealistic in practice. We investigate the emergence of new types of collective behavior in large collections of random events, where each event can, and will, influence all the others.