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Fredholm determinant representation of the Painlevé II $τ$-function (2008.01142v4)
Published 3 Aug 2020 in math-ph, math.CA, math.MP, and nlin.SI
Abstract: We formulate the generic $\tau$-function of the Painlev\'e II equation as a Fredholm determinant of an integrable (Its-Izergin-Korepin-Slavnov) operator. The $\tau$-function depends on the isomonodromic time $t$ and two Stokes' parameters, and the vanishing locus of the $\tau$-function, called the Malgrange divisor is determined by the zeros of the Fredholm determinant.
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