Mathematical Sciences: Studies in Interacting Particle Systems

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The project will support research into a number of problems in probability theory. Liggett will consider several questions related to interacting particle systems: survival and extinction of contact processes in random environments, rates of convergence to equilibrium in the exclusion process, survival of the threshold voter model, and the limiting behavior of an infinite series of queues. Schonmann will consider problems in interacting particle systems and large deviations: metastability for stochastic Ising models, critical behavior of cellular automata, and large deviations for random fields. The principal investigators will conduct research on several problems in probability theory. The primary focus will be on interacting systems of particles. These systems arise in modeling physical and biological systems, and have applications in other areas, such as computer science.