For random unitary pencils, the large-dimension limit of the determinant correlation integral equals det(I⊗I − Σ X_j⊗\bar{Y}_j)^{-1} when the coefficient tuples have outer spectral radius below 1, proved exactly for scalar coefficients and for upper-triangular coefficient matrices.
On the averages of characteristic polynomials from classical groups.Comm
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Determinants of Random Unitary Pencils
For random unitary pencils, the large-dimension limit of the determinant correlation integral equals det(I⊗I − Σ X_j⊗\bar{Y}_j)^{-1} when the coefficient tuples have outer spectral radius below 1, proved exactly for scalar coefficients and for upper-triangular coefficient matrices.