Double scaling limit in the random matrix model: The Riemann-Hilbert approach

DOI10.1002/cpa.10065zbMath1032.82014arXivmath-ph/0201003OpenAlexW2060987607MaRDI QIDQ4425970

Publication date: 15 September 2003

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0201003

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Boundary value problems in the complex plane (30E25) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

Related Items

The Hermitian two matrix model with an even quartic potential, The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1], Location of poles for the Hastings-McLeod solution to the second Painlevé equation, Gravitational lensing by eigenvalue distributions of random matrix models, Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials, Lectures on Random Matrix Models, Large N Asymptotics in Random Matrices, Large \(n\) limit of Gaussian random matrices with external source. I, Universality of a double scaling limit near singular edge points in random matrix models, A critical phenomenon in the two-matrix model in the quartic/quadratic case, The sine-law gap probability, Painlevé 5, and asymptotic expansion by the topological recursion, Propagation of singular behavior for Gaussian perturbations of random matrices, Universality in the two‐matrix model: a Riemann‐Hilbert steepest‐descent analysis, Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane, A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality, Double scaling and finite size corrections in \(\mathfrak{sl}(2)\) spin chain, Exact solution of the six-vertex model with domain wall boundary conditions. Disordered phase, Large \(n\) limit of Gaussian random matrices with external source. III: Double scaling limit, Properties of generalized Freud polynomials, A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions, Phase diagram and topological expansion in the complex quartic random matrix model, Fractional-superstring amplitudes, multi-cut matrix models and non-critical M theory, A matrix model for flat space quantum gravity, Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials, ASYMPTOTIC EXPANSIONS FOR RIEMANN–HILBERT PROBLEMS, Orthogonal and symplectic matrix models: universality and other properties, Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system, Asymptotics of a Fredholm determinant corresponding to the first bulk critical universality class in random matrix models, Stokes phenomena and non-perturbative completion in the multi-cut two-matrix models, Double scaling limit for matrix models with nonanalytic potentials, Painlevé kernels in Hermitian matrix models, Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies, Determination ofS-curves with applications to the theory of non-Hermitian orthogonal polynomials, Equilibrium measures in the presence of certain rational external fields, On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight, On external fields created by fixed charges, Some open problems in random matrix theory and the theory of integrable systems. II, Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I, Extremes of \(N\) vicious walkers for large \(N\): application to the directed polymer and KPZ interfaces, Change of variables as a method to study general β-models: Bulk universality, Riemann-Hilbert analysis and uniform convergence of rational interpolants to the exponential function, On tronquée solutions of the first Painlevé hierarchy, On properties of a deformed Freud weight, Numerical study of a multiscale expansion of the Korteweg–de Vries equation and Painlevé-II equation, Random matrix model with external source and a constrained vector equilibrium problem, Phase transitions and equilibrium measures in random matrix models, A matrix model with a singular weight and Painlevé III, Asymptotics for the partition function in two-cut random matrix models, Introduction, Global asymptotic expansions of the Laguerre polynomials -- a Riemann-Hilbert approach, Painlevé XXXIV Asymptotics of Orthogonal Polynomials for the Gaussian Weight with a Jump at the Edge, Painlevé IV Asymptotics for Orthogonal Polynomials with Respect to a Modified Laguerre Weight, Two Lax systems for the Painlevé II Equation, and Two Related Kernels in Random Matrix Theory, Phase transitions for deformations of JT supergravity and matrix models, Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit, Asymptotics of the partition function of a random matrix model., Large \(n\) limit of Gaussian random matrices with external source. II, Asymptotics of a cubic sine kernel determinant, Phase structure and asymptotic zero densities of orthogonal polynomials in the cubic model, On the joint distribution of the maximum and its position of the Airy2 process minus a parabola, Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation, Painlevé II in random matrix theory and related fields, New multicritical random matrix ensembles

Cites Work