CAREER: Mean Field Spin Glasses and Related Applications

职业：平均场旋转玻璃及相关应用

• 批准号: 1752184
• 负责人: Wei-Kuo Chen
• 金额: $ 40万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1752184&HistoricalAwards=false
• 关键词: CAREER; Mean; Field; Spin; Glasses

In the 1970s theoretical physicists invented a number of statistical mechanical models, called spin glasses, in order to study the strange behavior of certain alloys, such as CuMn. In mathematics, they are purely probabilistic objects possessing extremely intricate dependence structures and exhibit several crucial features that are commonly shared in many randomized combinatorial systems arising from various scientific fields. As a result, spin glass models are very often cited as examples of complex systems and the corresponding research has been of great use in understanding many real-world problems emerging from, such as, computer science, data science, and many others. This project aims to improve the current mathematical understanding of the mean field spin glass models and to establish theoretical foundations for related applications in data science. An integral part of the project is the development of educational activities including mentoring graduate students and postdoc fellows, developing advanced courses, and supervising undergraduate summer research. The project involves the study of the structure of the functional order parameter and its connection to the fluctuation and the energy landscape of the mean field spin glasses. In addition, the PI plans to investigate the mean field spin glass models by means of the classical statistical mechanics based on the Thouless-Anderson-Palmer approach and analyze its relation to the Parisi theory. The PI will also study spin glass models with more complicated dependence structures including the bipartite model and the Levy spin glass. Furthermore, the PI intends to study some randomized combinatorial optimization problems arising from data science in the approach of spin glass theory such as the detection problems and positive semi-definite programming. Based on these research projects, the educational component involves organizing probability summer programs and mentoring graduate, undergraduate students as well as postdoc fellows.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.

在1970年代，理论物理学家发明了许多称为自旋眼镜的统计机械模型，以研究某些合金的奇怪行为，例如Cumn。在数学中，它们是具有极其复杂的依赖性结构的纯粹概率对象，并且表现出了几种至关重要的特征，这些特征通常在许多由各种科学领域引起的随机组合系统中共享。结果，经常将自旋玻璃模型作为复杂系统的示例，相应的研究在理解许多现实世界中出现的问题（例如计算机科学，数据科学等）都有很大的用途。该项目旨在提高对平均场旋转玻璃模型的当前数学理解，并为数据科学中相关应用建立理论基础。该项目不可或缺的一部分是开发教育活动，包括指导研究生和博士后研究员，开发高级课程以及监督本科夏季研究。该项目涉及对功能顺序参数的结构的研究及其与平均场旋光玻璃的波动和能量景观的联系。此外，PI计划通过基于Thou-Anderson-Palmer方法的经典统计力学来研究平均田间自旋玻璃模型，并分析其与Parisi理论的关系。 PI还将研究具有更复杂依赖性结构的自旋玻璃模型，包括两部分模型和征税自旋玻璃。此外，PI打算研究旋转玻璃理论方法中数据科学引起的一些随机组合优化问题，例如检测问题和阳性半明确编程。基于这些研究项目，教育部分涉及组织概率夏季计划，并指导毕业生，本科生以及博士后研究员。该奖项反映了NSF的法定任务，并被认为值得通过基金会的知识分子优点和更广泛的影响来通过评估来获得支持。

项目成果

On the Almeida-Thouless transition line in the Sherrington-Kirkpatrick model with centered Gaussian external field

中心高斯外场 Sherrington-Kirkpatrick 模型中的 Almeida-Thouless 过渡线

• DOI: 10.1214/21-ecp439
• 发表时间: 2021
• 期刊: Electronic Communications in Probability
• 影响因子: 0.5
• 作者: Chen, Wei-Kuo

The Generalized TAP Free Energy II

广义 TAP 自由能 II

• DOI: 10.1007/s00220-020-03887-x
• 发表时间: 2021
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Chen, Wei-Kuo;Panchenko, Dmitry;Subag, Eliran
• 通讯作者: Subag, Eliran

Order of fluctuations of the free energyin the SK model at critical temperature

临界温度下SK模型自由能涨落顺序

• DOI: 10.30757/alea.v16-29
• 发表时间: 2019
• 期刊: Latin American Journal of Probability and Mathematical Statistics
• 作者: Chen, Wei-Kuo;Lam, Wai-Kit
• 通讯作者: Lam, Wai-Kit

On Convergence of the Cavity and Bolthausen’s TAP Iterations to the Local Magnetization

关于腔和 Bolthausen 的 TAP 迭代对局部磁化强度的收敛

• DOI: 10.1007/s00220-021-04103-0
• 发表时间: 2021
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Chen, Wei-Kuo;Tang, Si
• 通讯作者: Tang, Si

Generalized TAP Free Energy

广义TAP自由能

• DOI: 10.1002/cpa.22040
• 发表时间: 2022
• 期刊: Communications on Pure and Applied Mathematics
• 影响因子: 3
• 作者: Chen, Wei‐Kuo;Panchenko, Dmitry;Subag, Eliran
• 通讯作者: Subag, Eliran