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Applied Math Seminar
Applied Stochastic Analysis (or Applied Random Matrix Theory)
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What is the next term in the following sequence? scalars, vectors, .... ? Yes matrices. Current random matrix theory is the natural next step in the sequence that starts with classical statistics, then moves up to multivariate statistics, and now we have "matrix statistics" with all of the theoretical problems, new exciting applications, and numerical algorithmic techniques one would expect. Only random matrix theory has new more complicated aspects, yet is mathematically rich. In this talk we will survey how random matrix theory is being picked up and used in so many applied areas. We will discuss connections to orthogonal polynomials. We will explain how the polynomial method is allowing a wide range of computations. We will conclude with a simple and more general derivation of an eigenvalue density ("level density" ) formula. Summary: probability + linear algebra, how could it not be useful? |