Several P. Investigators. They apply techniques learned from the study of genetics and random permutations, including couplings, the total variation distance and Wasserstein metric for processes observing some or all of the possible component sizes, size-biased permutations of the components, sampling properties for populations, and Stein's method. The interaction between pure and applied method can be fruitful for both.
Techniques motivated by the needs and intuitions from each field can illuminate the other.
For example, the applied study of genetics naturally involves sampling from populations, which leads to the notion of a size- biased permutation, which simplifies the understanding of a question from pure math, involving the large prime factors of a random integer. The proposed investigation attempts to straddle the boundary between pure and applied math as it relates to genetics, sampling, and prime numbers. . . . More on THIS Work .