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On the connection problem for Painlev\'e I

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arxiv 1612.08382 v1 pith:IWEIJUAW submitted 2016-12-26 nlin.SI math-phmath.CAmath.MP

O. Lisovyy , J. Roussillon This is my paper
classification nlin.SImath-phmath.CAmath.MP
keywords connectionfunctionpainlevproblemassociatedasymptoticscanonicalcluster
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We study the dependence of the tau function of Painlev\'e 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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Many-faced Painlev\'e I: irregular conformal blocks, topological recursion, and holomorphic anomaly approaches

    math-ph 2025-05 conditional novelty 7.0 of 10

    The paper proves the conifold gap property for Weierstrass elliptic topological recursion and gives an algebraic construction of the rank 5/2 Virasoro Whittaker state, linking the Painlevé I tau function to CFT and ho...

  2. Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations

    math-ph 2025-12 unverdicted novelty 3.0 of 10

    Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.

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