<Previous Article In Issue
Volume 9, Issue 4, November 2002, Pages 530 - 550
On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices
Authors
J. Harnad
Corresponding Author
J. Harnad
Received 11 May 2002, Revised 29 May 2002, Accepted 12 June 2002, Available Online 1 November 2002.
- DOI
- 10.2991/jnmp.2002.9.4.11How to use a DOI?
- 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 Riemann sphere and interpret the Fredholm determinants as isomonodromic -functions.
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
<Previous Article In Issue
Cite this article
TY - JOUR AU - J. Harnad PY - 2002 DA - 2002/11/01 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 - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.4.11 DO - 10.2991/jnmp.2002.9.4.11 ID - Harnad2002 ER -