Volume 9, Issue 4, November 2001, Pages 530 - 550
On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices
- J HARNAD
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- J HARNAD
Available Online 9 December 2006.
- https://doi.org/10.2991/jnmp.2002.9.4.11How to use a DOI?
- 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 Riemann sphere and interpret the Fredholm determinants as isomonodromic -functions.
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TY - JOUR AU - J HARNAD PY - 2006 DA - 2006/12 TI - On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices JO - Journal of Nonlinear Mathematical Physics SP - 530 EP - 550 VL - 9 IS - 4 SN - 1402-9251 UR - https://doi.org/10.2991/jnmp.2002.9.4.11 DO - https://doi.org/10.2991/jnmp.2002.9.4.11 ID - HARNAD2006 ER -