Random Matrices with External Source and Multiple Orthogonal Polynomials
نویسندگان
چکیده
defined on n× nHermitian matricesM. The ensemble (1.1) consists of a general unitary invariant part V(M) and an extra termAM,whereA is a fixed n×nHermitianmatrix, the external source or the external field. Due to the external source, the ensemble (1.1) is not unitary invariant. For the special Gaussian case V(x) = (1/2)x, we can write M in (1.1) asM = H+A,whereH is a randommatrix from the GUE ensemble andA is deterministic, hence in this case it reduces to the class of deterministic plus random matrices studied in [5, 6, 7, 8, 9, 10, 18]. Zinn-Justin [20] showed that the eigenvalue correlations of ensemble (1.1) can be expressed in the determinantal form
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