Mathematical Sciences: Spectral Theory for Large DimensionalRandom Matrices

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The topic of research is the asymptotic theory of spectra for large random matrices. The types of matrices to be studied include square matrices whose entries are independent identically distributed random variables, symmetric matrices for which various entries are mutually independent, and matrices of a sort that are covariance matrices in special cases. For each of these types of matrices problems that involve the asymptotic spectral distribution of the random matrix and problems that involve the asymptotic behavior of the extremal eigenvalues for the random matrix will be studied.