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Spin Glasses and Other Models of Disordered Media

自旋玻璃和其他无序介质模型

基本信息

批准号：
2154076
负责人：
Antonio Auffinger
金额：
$ 33.81万
依托单位：
Northwestern University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-07-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2154076&HistoricalAwards=false
关键词：
Spin Glasses Other Models Disordered

项目摘要

One of the main goals of probability theory is to understand how a large number individuals and their small interactions translate to novel behavior of an entire system. The goal of this project is to analyze such complex disordered systems where the interactions have high-dimensional dependence structures and where the extremes (low energy configurations, optimal trajectories) play a significant role. As well as being important to probability theory, the results to be obtained in this project will be relevant and applied to many branches of science, as most of the questions were introduced to understand the behavior of various optimization problems in physics, computer science, theoretical biology, and social networks. Many of these projects are in collaboration with graduate students; the PI will continue mentoring and training of students and post-doctoral researchers. The project concerns problems on mean field spin glass models and on first-passage percolation models. Those problems include a study to quantify the low-temperature structure of mean field spin glass models, with the long range goal of rigorously establish the Parisi description of full replica symmetry breaking, to study limit shapes, fluctuations and geodesics rays in first passage percolation beyond the classical case of the integer lattice and to establish further properties on the number of stable and unstable equilibria in a class of random dynamical systems.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.

概率论的主要目标之一是理解大量个体及其微小的相互作用如何转化为整个系统的新行为。该项目的目标是分析这种复杂的无序系统，其中相互作用具有高维依赖结构，并且极端（低能量配置，最佳轨迹）发挥着重要作用。除了对概率论很重要之外，这个项目中获得的结果将与许多科学分支相关并应用于许多科学分支，因为大多数问题都是为了理解物理学，计算机科学，理论生物学和社交网络中各种优化问题的行为而引入的。其中许多项目是与研究生合作的; PI将继续指导和培训学生和博士后研究人员。该项目涉及平均场自旋玻璃模型和首次通过渗流模型的问题。这些问题包括研究量化平均场自旋玻璃模型的低温结构，长期目标是严格建立完全复制对称性破缺的Parisi描述，研究极限形状，波动和测地线射线在第一次通过渗流超越经典情况下的整数格，并建立进一步的性质的数目稳定和不稳定的平衡，在一类随机动力系统。该奖项反映了NSF的法定使命，并且通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。