On the bilinear equations for Fredholm determinants appearing in random matrices

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dc.creatorHarnad, J.
dc.date1999-06-10
dc.date2003-06-17
dc.date.accessioned2026-07-07T06:17:50Z
dc.date.available2026-07-07T06:17:50Z
dc.descriptionIt 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 $τ$-functions.
dc.descriptionarxiv version is already official
dc.identifierhttps://arxiv.org/abs/solv-int/9906004
dc.identifierhttp://arxiv.org/abs/solv-int/9906004
dc.identifierJ. Nonlinear Math. Phys., volume 9, no. 4 (2002) 530-550
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/94525
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleOn the bilinear equations for Fredholm determinants appearing in random matrices
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