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John Harnad - The bilinear differential equations satisfied by Fredholm determinants appearing in random matrices
| JOHN HARNAD, Concordia University |
| The bilinear differential equations satisfied by Fredholm determinants appearing in random matrices |
Bilinear differential equations satisfied by the Fredholm determinants
of certain integral operators appearing as spectral distribution
functions for random matrices are 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 express the latter as isomonodromic deformation equations
for families of rational covariant derivative operators on the Riemann
sphere and to interpret the Fredholm determinants as isomonodromic
-functions.
