A Factorization of Determinant Related to Some Random Matrices

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Abstract

We consider the expectation of the determinant det(λ−X)−1 for Im λ>0 associated with some random N×N matrices and factorize it into N Stieltjes transforms of probability measures. Moreover, using this factorization, we investigate the limiting behavior of the logarithm of the quantity as N→∞.

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