An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model

DOI10.1016/j.nuclphysb.2011.02.019zbMath1215.82024arXiv1101.2727OpenAlexW2137740584MaRDI QIDQ545245

Gabriel Álvarez, Elena Medina, Luis Martínez-Alonso

Publication date: 22 June 2011

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.2727

zbMATH Keywords

genus expansioncounting mapsHermitian matrix model

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Random matrices (algebraic aspects) (15B52) Other special orthogonal polynomials and functions (33C47) Statistical thermodynamics (82B30)

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Cites Work

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• Matrix models as CFT: genus expansion
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Random matrices, graphical enumeration and the continuum limit of Toda lattices
• Nonpertubative effects and the large-order behavior of matrix models and topological strings
• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• Quantum field theory techniques in graphical enumeration
• Level-spacing distributions and the Airy kernel
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Planar diagrams
• Generating functions in two-dimensional quantum gravity
• Matrix model calculations beyond the spherical limit.
• Asymptotics of the partition function of a random matrix model.
• Caustics, counting maps and semi-classical asymptotics
• Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• Generic behavior of the density of states in random matrix theory and equilibrium problems in the presence of real analytic external fields
• Breakdown of universality in multi-cut matrix models
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• The planar approximation. II
• Universal distribution of random matrix eigenvalues near the ‘birth of a cut’ transition
• A new type of critical behaviour in random matrix models
• Semiclassical expansions in the Toda hierarchy and the Hermitian matrix model