Painlevé kernels in Hermitian matrix models

2013/02/07 by Maurice Duits, Duits, Maurice · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.CV #math.MP

paper · pdf · doi:10.48550/arxiv.1302.1710

26 pages, 5 figures; This is a contribution to the Special Issue on Painlevé equations in the journal Constructive Approximation

arxiv created 2013/02/07 · openalex publication_date 2013/02/07 · arxiv updated 2013/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After reviewing the Hermitian one matrix model, we will give a brief introduction to the Hermitian two matrix model and present a summary of some recent results on the asymptotic behavior of the two matrix model with a quartic potential. In particular, we will discuss a limiting kernel in the quartic/quadratic case that is constructed out of a 4× 4 Riemann-Hilbert problem related to Painlevé II equation. Also an open problem will be presented.

Cited by

• Asymptotics for the noncommutative Painlevé II equation

Related

• A Riemann-Hilbert problem for equations of Painlevé type in the one matrix model with semi-classical potential
• Two Lax systems for the Painlevé II equation, and two related kernels in random matrix theory
• Asymptotic analysis of the two matrix model with a quartic potential
• Double scaling limit in the random matrix model: the Riemann-Hilbert approach
• The Hermitian two matrix model with an even quartic potential