Total integrals of global solutions to Painlevé II

DOI10.1088/0951-7715/22/5/006zbMath1179.33036arXiv0810.2586OpenAlexW2086527469MaRDI QIDQ3628729

Jeffery C. DiFranco, Robert J. Buckingham, Alexander R. Its, Jinho Baik

Publication date: 20 May 2009

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.2586

zbMATH Keywords

asymptotic expansionPainlevé equationRiemann-Hilbert problemrandom matrixtrace formulaetotal integral

Mathematics Subject Classification ID

Random matrices (algebraic aspects) (15B52) Riemann-Hilbert problems in context of PDEs (35Q15) Painlevé-type functions (33E17)

Related Items (13)

Monodromy dependence and connection formulae for isomonodromic tau functions ⋮ Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge ⋮ The asymptotics of a Bessel-kernel determinant which arises in random matrix theory ⋮ On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation ⋮ Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation ⋮ Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant ⋮ On Some Hamiltonian Properties of the Isomonodromic Tau Functions ⋮ Large deformations of the Tracy-Widom distribution. I: Non-oscillatory asymptotics ⋮ On the increasing tritronquée solutions of the Painlevé-II equation ⋮ Asymptotics of integrals of some functions related to the degenerate third Painlevé equation ⋮ Double Spiral Singularities for a Flow of Regular Planar Curves ⋮ Edge distribution of thinned real eigenvalues in the real Ginibre ensemble ⋮ On global solutions of defocusing mKdV equation with specific initial data of critical regularity

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