Transition asymptotics for the Painlevé II transcendent

DOI10.1215/00127094-3714650zbMath1369.34107arXiv1502.03402OpenAlexW2020998610MaRDI QIDQ516141

Thomas Bothner

Publication date: 22 March 2017

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.03402

zbMATH Keywords

Riemann-Hilbert problemsecond Painlevé equationDeift-Zhou nonlinear steepest descent methodtransition asymptotics

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Asymptotic properties of solutions to ordinary differential equations (34D05) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Asymptotic expansions of solutions to ordinary differential equations (34E05) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (14)

Global rigidity and exponential moments for soft and hard edge point processes ⋮ Open problems for Painlevé equations ⋮ Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge ⋮ Lower tail of the KPZ equation ⋮ Determinantal point processes conditioned on randomly incomplete configurations ⋮ Probability of two large gaps in the bulk and at the edge of the spectrum of random matrices ⋮ The lower tail of the half-space KPZ equation ⋮ Large deformations of the Tracy-Widom distribution. I: Non-oscillatory asymptotics ⋮ On the increasing tritronquée solutions of the Painlevé-II equation ⋮ The τ-function of the Ablowitz-Segur family of solutions to Painlevé II as a Widom constant ⋮ Connection formulas for the Ablowitz–Segur solutions of the inhomogeneous Painlevé II equation ⋮ On the origins of Riemann–Hilbert problems in mathematics* ⋮ Fredholm determinant representation of the homogeneous Painlevé II τ-function ⋮ Resurgent trans-series for generalized Hastings–McLeod solutions

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