Fredholm determinant representation of the homogeneous Painlevé II τ-function

We formulate the generic tau-function of the homogeneous Painleve 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. The vanishing locus of the tau-function, called the Malgrange divisor is then determined by the zeros of the Fredholm determinant.