Abstract
An identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables are used to show that the ensemble average ofS different pairs of eigenvalues of a GOE is given by (−1)S2−Sπ−1/2Γ(S+1/2).
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Communicated by H. Araki
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Ullah, N. Ensemble average of an arbitrary number of pairs of different eigenvalues using Grassmann integration. Commun.Math. Phys. 104, 693–695 (1986). https://doi.org/10.1007/BF01211071
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DOI: https://doi.org/10.1007/BF01211071