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Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory

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arxiv math-ph/0111007 v1 pith:2E6TKR3S submitted 2001-11-05 math-ph math.CAmath.MPmath.RT

Alexei Borodin , Percy Deift This is my paper · ORCID
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The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equations. Their methods are based on the theory of integrable operators and the theory of Riemann-Hilbert problems.

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Cited by 1 Pith paper

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  1. Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution

    math-ph 2026-03 conditional novelty 7.0 of 10

    The full persistence distribution in 1D Ising coarsening equals a Pfaffian Fredholm determinant of the sech kernel and is controlled by a Painlevé VI equation that is the mean curvature of a Bonnet surface.

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