Mathematical Sciences: Discrete Probability Theory and Associated Limit Theorems

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A Research Experiences for Undergraduates site involving six students will be supported by this award. Their work will focus on carefully selected problems in applied probability. Students will be expected to combine collaborative and individual efforts in their research. At the end of the summer, the group will travel to a professional meeting such as the Institute for Mathematical Statistics/American Statistical Association joint meetings. Students are expected to prepare written reports summarizing their work, many of which should lead to publishable papers. They will be encouraged to present their findings either at meetings or at their home institutions. The theme of the research is that of discrete probability structures such as occurrence patterns and runs, competition models or occupancy problems. Principal focus will be on the application of the Stein-Chen method of Poisson approximation, but students will also consider Gaussian limits and other non- Poisson approximations.