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.
J.,Relationships betweenτ-functions and Fredholm determinant expressions for gap probabilities in random matrix theory, Nonlinearity 19, 1643—1656 (2006)
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Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution
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.