Spin Glasses: A New Direction for Probability Theory

自旋玻璃：概率论的新方向

• 批准号: 9988480
• 负责人: Michel Talagrand
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9988480&HistoricalAwards=false
• 关键词: Spin; Glasses; New; Direction; Probability

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.

9988480塔拉格兰德在研究自旋玻璃的平均场模型（如著名的谢林顿柯克帕特里克模型）时，一些物理学家“发现”（或者更准确地说，是发现）了概率论中的一些全新现象，即在相关随机变量的大家族的极值附近存在复杂的结构。本研究的主要目的是通过对主要模型的研究，为它们的构造提供严格的数学基础。两个主要目标是控制主要模型的整个高温区域，以及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从大量随机事件中出现一种有序。这是表达的主要经典定理，从大数定律开始。这些经典结果涉及事件相互独立，即相互不影响的情况。这种假设在实践中是不现实的。我们研究了在大量随机事件中出现的新型集体行为，其中每个事件都可以并且将会影响所有其他事件。