On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices

  title={On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices},
  author={J. Harnad},
  journal={Journal of Nonlinear Mathematical Physics},
  pages={530 - 550}
  • J. Harnad
  • Published 10 June 1999
  • Mathematics
  • Journal of Nonlinear Mathematical Physics
Abstract It is shown how the bilinear differential equations satisfied by Fredholm determinants of integral operators appearing as spectral distribution functions for random matrices may be deduced from the associated systems of nonautonomous Hamiltonian equations satisfied by auxiliary canonical phase space variables introduced by Tracy and Widom. The essential step is to recast the latter as isomonodromic deformation equations for families of rational covariant derivative operators on the… 

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