Random Matrices, Spin Glass, and Interacting Particle Systems

许多物理现象被模拟为粒子随机相互作用。在单车道交通中移动汽车就是这样的例子之一。有时候，小区域内粒子的相互作用会随着时间的推移对远处的位置产生持久的影响。了解这种影响的传播速度是非常有趣的。这个项目关注的是一类随机过程的局部随机相互作用在全球范围内的传播的一些基本问题。该项目为本科生和研究生提供研究培训机会。具体而言，研究员将对自旋玻璃、相互作用粒子系统和随机增长模型进行研究，重点关注大系统的波动。特别地，研究者将研究具有临界调谐外场的双自旋球形Sherrington-Kirkpatrick模型的自由能和重叠，周期KPZ普适类的随机场，以及一类定向渗流模型的最后通过时间。有深刻的联系，以随机矩阵理论，调查人员将利用，也扩大。该奖项反映了NSF的法定使命，并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。

Many physical phenomena are modeled as particles interacting randomly. Moving cars in one-lane traffic are one of such examples. Sometimes the interactions of the particles in a small area have a lasting influence on the far away location over time. It is of great interest to find out how fast such influence spreads. This project is concerned with some of the fundamental questions on the spread of local random interactions on a global scale for a class of random processes. The project provides research training opportunities for both undergraduate and graduate students.In more concrete terms, the investigator will perform research on spin glass, interacting particle systems, and random growth models with a focus on the fluctuations of large systems. In particular, the investigator will study the free energy and overlaps of the two-spin spherical Sherrington-Kirkpatrick model with critically-tuned external field, the random field for periodic KPZ universality class, and also the last passage time for a class of directed percolation models. There are deep connections to random matrix theory which the investigator will utilize and also expand. The exactly solvable nature of the models will also be used in the research.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.