Journal of Nonlinear Mathematical Physics

Volume 9, Issue 4, November 2001, Pages 530 - 550

On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices

Authors
J HARNAD
Corresponding Author
J HARNAD
Available Online 9 December 2006.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 4
Pages
530 - 550
Publication Date
2006/12
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.4.11How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

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  -