Random Matrix Theory and Computations

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The PI will study major problem in random matrix theory and theirapplications. One question is what mathematical abstractions areresponsible for the universality of random matrix theory formulas.The PI will investigate whether a certain stochastic Hermitian operator will yield new insights. This point of view allows the study of general beta formulas beyond the traditional beta=1,2, and 4available in much of classical random matrix theory. As part of this project we will produce software for random matrix integrals,Jack polynomials, and orthogonal polynomials of matrix argument.Random matrix theory is becoming increasingly important as the formulasthat were obtained in this once esoteric field are now findingapplication in areas as far reaching as array processing, numericalanalysis, computational complexity, and traditional fields of mathematics and physics including combinatorics, integrable-systems,and so many other fields. This is randomized "linear algebra."The random matrix techniques developed today will become importanttools for scientists and engineers in the coming decade.