Universal distribution of random matrix eigenvalues near the ‘birth of a cut’ transition

DOI10.1088/1742-5468/2006/07/P07005zbMath1456.81372arXivmath-ph/0605064MaRDI QIDQ5239294

Bertrand Eynard

Publication date: 22 October 2019

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0605064

zbMATH Keywords

conformal field theorymatrix models

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52)

Related Items (9)

Superpotentials, quantum parameter space and phase transitions in \( \mathcal{N}=1\) supersymmetric gauge theories ⋮ A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions ⋮ Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies ⋮ Boutroux curves with external field: equilibrium measures without a variational problem ⋮ An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model ⋮ Phase transitions and equilibrium measures in random matrix models ⋮ A matrix model for plane partitions ⋮ A new type of critical behaviour in random matrix models ⋮ All order asymptotic expansion of large partitions

Cites Work

• Conformal field theory
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Theta functions on Riemann surfaces
• Planar diagrams
• Rational theories of \(2\)d gravity from the two-matrix model.
• On fluctuations of eigenvalues of random Hermitian matrices.
• Correlations between eigenvalues of a random matrix
• Double scaling limit in random matrix models and a nonlinear hierarchy of differential equations
• Breakdown of universality in multi-cut matrix models
• LOOP EQUATIONS AND THE TOPOLOGICAL PHASE OF MULTI-CUT MATRIX MODELS
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
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