Mathematical Sciences: Interacting Particle Systems and Random Cellular Automata

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This research effort will focus on the analysis of interacting particle systems with simple dynamics that exhibit large-scale self-organized behavior. Initially, the research will focus on two families of models, in the plane and in space, with random cyclic dynamics: the cyclic cellular automata, and the cyclic particle system. The models are prototypes for spatial interactive wave phenomena observed in certain chemical reactions, atrial fibrillation, neural networks, and elsewhere. Following these investigations, the research will involve other interacting systems such as 'anti-stepping stone models' and various one-dimensional interface dynamics. This research is in the general area of probability theory known as interacting particle systems. Such systems, and related cellular automata, model complex random dynamics. They have found application in a wide variety of scientific contexts, including physics, chemistry, biology, and computer science. Of special importance are their connections with statistical physics, population genetics, and information transmission.