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Thursday, October 7, 2021

**Abstract:** It was mentioned in previous talks that bounding distance between two distributions in appropriate metric is often equivalent to finding a good coupling of random variables. In this talk we will build up on that idea and study the use of couplings in bounding total variation distance between two counting random variables. We will apply these techniques to head runs in a sequence of independent coin tosses and occupancy problem as well as other models if time permits. This talk serves as introduction to the Chen-Stein method for Poisson approximation, on which we will focus in the second talk.