Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations

DOI10.1007/s00023-019-00834-yzbMath1467.37057arXiv1809.07074OpenAlexW3102098981MaRDI QIDQ2273633

Lun Zhang, Dan Dai, Shuai-Xia Xu

Publication date: 24 September 2019

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.07074

zbMATH Keywords

second Painlevé equationrandom matrixtronquée solution

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Random matrices (algebraic aspects) (15B52) Painlevé-type functions (33E17) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65)

Related Items

Laguerre unitary ensembles with jump discontinuities, PDEs and the coupled Painlevé V system ⋮ Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble ⋮ Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation

Uses Software

• DLMF

Cites Work

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• Tau-function theory of chaotic quantum transport with \(\beta = 1, 2, 4\)
• Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
• The isomonodromy approach to matrix models in 2D quantum gravity
• Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
• Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I.
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• A matrix model with a singular weight and Painlevé III
• Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge
• On an Average over the Gaussian Unitary Ensemble
• Critical Edge Behavior in Unitary Random Matrix Ensembles and the Thirty-Fourth Painlevé Transcendent
• Tuck's incompressibility function: statistics for zeta zeros and eigenvalues
• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
• Random Matrix Ensembles with Singularities and a Hierarchy of Painlevé III Equations
• Gap Probability at the Hard Edge for Random Matrix Ensembles with Pole Singularities in the Potential
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• The generating function for the Bessel point process and a system of coupled Painlevé V equations
• The Lenard Recursion Relation and a Family of Singularly Perturbed Matrix Models
• The Generating Function for the Airy Point Process and a System of Coupled Painlevé II Equations

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