Two Lax systems for the Painlevé II Equation, and Two Related Kernels in Random Matrix Theory

DOI10.1137/16M1056080zbMath1353.34111arXiv1601.01603OpenAlexW2963035718MaRDI QIDQ2827754

Dong Wang, Karl Liechty

Publication date: 21 October 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01603

zbMATH Keywords

Painlevé II equationLax pairdeterminantal point processtacnode Riemann-Hilbert problem

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17)

Related Items

Nonintersecting Brownian bridges between reflecting or absorbing walls ⋮ The \(k\)-tacnode process

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonintersecting Brownian motions on the unit circle
• A critical phenomenon in the two-matrix model in the quartic/quadratic case
• Nonintersecting random walks in the neighborhood of a symmetric tacnode
• Non-intersecting squared Bessel paths at a hard-edge tacnode
• Non-colliding Brownian bridges and the asymmetric tacnode process
• Painlevé kernels in Hermitian matrix models
• The tacnode Riemann-Hilbert problem
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Monodromy- and spectrum-preserving deformations. I
• Level-spacing distributions and the Airy kernel
• On orthogonal and symplectic matrix ensembles
• Non-colliding Brownian motions and the extended tacnode process
• Multi-critical unitary random matrix ensembles and the general Painlevé II equation
• Double Aztec diamonds and the tacnode process
• Universality and critical behaviour in the chiral two-matrix model
• On the joint distribution of the maximum and its position of the Airy2 process minus a parabola
• Critical behavior of nonintersecting Brownian motions at a tacnode
• Universality of the double scaling limit in random matrix models
• On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system
• On the linearization of the first and second Painlevé equations
• Double scaling limit in the random matrix model: The Riemann-Hilbert approach
• The Tacnode Kernel: Equality of Riemann–Hilbert and Airy Resolvent Formulas
• Asymptotics for the painlevé II equation
• Integrals of nonlinear equations of evolution and solitary waves

This page was built for publication: Two Lax systems for the Painlevé II Equation, and Two Related Kernels in Random Matrix Theory