Abstract
We consider the expectation of the determinant det(λ−X)−1for Im λ>0 associated with some random N×Nmatrices and factorize it into NStieltjes 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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Shirai, T. A Factorization of Determinant Related to Some Random Matrices. Journal of Statistical Physics 90, 1449–1459 (1998). https://doi.org/10.1023/A:1023252000178
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DOI: https://doi.org/10.1023/A:1023252000178