Kardar-Parisi-Zhang Universality Class, Integrable Differential Equations, and Spin Glass

Kardar-Parisi-Zhang 普适类、可积微分方程和自旋玻璃

• 批准号: 2246790
• 负责人: Jinho Baik
• 金额: $ 40.87万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2246790&HistoricalAwards=false
• 关键词: Kardar; Parisi; Zhang; Universality; Class

This project is about how sometimes complex and random interactions between the constituents in a large probabilistic system may lead to simple and universal behaviors. Here universality means that these properties are attained for a large class of such systems. A few concrete classes of probabilistic models and their fundamental properties will be investigated, especially when the system sizes become large. This project will help improve our understanding of the scopes and limitations of the universality of probability models. Many parts of the project will be carried out with graduate students and young researchers, helping their professional development. In concrete terms, the Kardar-Parisi-Zhang (KPZ) universality class models will be studied as well as their connections to integrable differential equations, and spin glass models. Of particular interest will be the multi-time distributions of KPZ universality class models on the ring domain, to understand and broaden the relations between the KPZ models and integrable differential equations, and to study the fluctuations of the spherical Sherrington-Kirkpatrick model perturbed by a deterministic field.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这个项目是关于在一个大的概率系统中，成分之间复杂和随机的相互作用如何导致简单和普遍的行为。在这里，普适性意味着这些性质是为一大类这样的系统所获得的。一些具体的类的概率模型和它们的基本属性将被调查，特别是当系统的规模变得很大。这个项目将有助于提高我们对概率模型普适性的范围和局限性的理解。该项目的许多部分将与研究生和年轻研究人员一起进行，帮助他们的专业发展。具体而言，Kardar-Parisi-Zhang（KPZ）普适类模型将被研究，以及它们与可积微分方程和自旋玻璃模型的联系。特别感兴趣的是KPZ普适类模型在环域上的多时间分布，以理解和拓宽KPZ模型与可积微分方程之间的关系，并研究球面谢灵顿的波动该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识产权进行评估来支持。优点和更广泛的影响审查标准。