On the connection problem for Painlevé I

Abstract

We study the dependence of the tau function of Painlevé I equation on the generalized monodromy of the associated linear problem. In particular, we compute connection constants relating the tau function asymptotics on five canonical rays at infinity. The result is expressed in terms of dilogarithms of cluster type coordinates on the space of Stokes data.

13 pages, 2 figures

References in corpus (2)

• On Painlevé/gauge theory correspondence
• Monodromy dependence and connection formulae for isomonodromic tau functions

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• Quantum spectral problems and isomonodromic deformations
• Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus
• Resurgent Structure of the Topological String and the First Painlevé Equation
• Painlevé Kernels and Surface Defects at Strong Coupling