Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems

DOI10.1088/1361-6544/abc598zbMath1470.34238arXiv2002.11240OpenAlexW3007920736MaRDI QIDQ4986210

Xiao-Bo Wu, Shuai-Xia Xu

Publication date: 27 April 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.11240

zbMATH Keywords

orthogonal polynomialsrandom matricesasymptotic analysisPainlevé equationsRiemann-Hilbert problemsHankel determinants

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17)

Related Items (5)

Truncated Hermite polynomials ⋮ Hankel determinants for a Gaussian weight with Fisher–Hartwig singularities and generalized Painlevé IV equation ⋮ A two-component Sasa-Satsuma equation: large-time asymptotics on the line ⋮ Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system ⋮ Exponential moments for disk counting statistics of random normal matrices in the critical regime

Uses Software

• DLMF

Cites Work

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• Random matrices with merging singularities and the Painlevé V equation
• Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
• Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• The isomonodromy approach to matrix models in 2D quantum gravity
• Level-spacing distributions and the Airy kernel
• Fredholm determinants, differential equations and matrix models
• Four-dimensional Painlevé-type equations associated with ramified linear equations. III: Garnier systems and Fuji-Suzuki systems
• Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system
• Asymptotics for Hankel determinants associated to a Hermite weight with a varying discontinuity
• Large gap asymptotics for Airy kernel determinants with discontinuities
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge
• Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump
• Gaussian Unitary Ensemble with Boundary Spectrum Singularity and σ‐Form of the Painlevé II Equation
• On Some Hamiltonian Properties of the Isomonodromic Tau Functions
• Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight
• Four-dimensional Painlevé-type equations associated with ramified linear equations II: Sasano systems
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• Asymptotics of Hankel Determinants With a One-Cut Regular Potential and Fisher–Hartwig Singularities
• Finite Size Effects for Spacing Distributions in Random Matrix Theory: Circular Ensembles and Riemann Zeros
• Thinning and conditioning of the circular unitary ensemble
• The Generating Function for the Airy Point Process and a System of Coupled Painlevé II Equations
• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.

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