Random Matrices, Spin Glass, and Interacting Particle Systems

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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.