Mathematical Sciences: Complex Stochastic Systems

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This research project falls within the general research area of statistics and probability. Technically, the research will be in the areas of Markov processes, additive functionals, spatial point processes, interacting particle systems, percolation, and approximation of stochastic processes. The research in Markov processes will have applications to population genetics; the study of large deviations of additive functionals of Markov processes will be used in interacting particle systems and models of avalanche photodetection; the work on spatial point processes will be directed toward model development; and the approximation of stochastic processes will be significant in the approximation of models of large networks. All of the research topics in this project have important applications.