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Annals of Mathematics, II. Series Vol. 149, No. 3, pp. 921976 (1999) 

The spectrum of coupled random matricesM. Adler and P. van MoerbekeReview from Zentralblatt MATH: The authors explain ``how the integrable technology can be brought to bear to gain insight into the nature of the distribution of the spectrum of coupled Hermitian random matrices and the equations the associated probabilities satisfy''. In the Gaussian case the distribution of $M_i$, $i=1,2$, is proportional to $$\exp\bigl \{T_r (M^2_1+ M^2_22cM_1M_2) \bigr\}$$ where the $M_i$ are $n\times n$ matrices. The topics described involve biorthogonal polynomials, twoToda lattice, vertex operators, Virasoro algebra and many others. Reviewed by Alexei Khorunzhy Keywords: spectrum; Hermitian random matrices; biorthogonal polynomials; twoToda lattice; vertex operators; Virasoro algebra Classification (MSC2000): 15A52 81R50 17B68 17B69 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
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