Mathematical Sciences: Evolution of Interacting Particle Systems

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This research concerns the area of interacting particle systems in probability theory, the theory of random walks in random environments, and the understanding of branching processes. This project should contribute to understanding the general theory of particle systems, the rate of diffusion of random walks in random environments, and the limiting density of branching random walks. Work on particle systems dates to about 1970 and has been motivated by examples of such systems from the biological sciences, statistical mechanics, and cybernetics. Typically, large numbers of particles are assumed to interact according to some rule; one is interested in the limiting behavior of such systems after a long time. Basic systems such as the contact process, voter model, and coalescing and annihilating random walks are simple models for the propagation of a species, the spread of disease, or the state of a chemical reaction.