Semiclassical orthogonal polynomials , matrix models and isomonodromic tau functions 1

@inproceedings{Bertola2004SemiclassicalOP,
  title={Semiclassical orthogonal polynomials , matrix models and isomonodromic tau functions 1},
  author={Marco Bertola and B. Eynard and J. Harnad},
  year={2004}
}
The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such measures. These are shown to preserve the generalized monodromy of the associated rank-2 rational covariant derivative operators. The corresponding matrix models, consisting of unitarily diagonalizable matrices with spectra supported on these contours are… CONTINUE READING

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