Combinatorics of dispersionless integrable systems and universality in random matrix theory

DOI10.1007/s00220-009-0894-1zbMath1188.82029arXiv0811.0351OpenAlexW1999215941MaRDI QIDQ1048141

Yuji Kodama, Virgil U. Pierce

Publication date: 11 January 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.0351

zbMATH Keywords

universalitydispersionless integrable systemsFaber polynomials.Toda and Pfaff lattice hierarchies

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Exactly solvable models; Bethe ansatz (82B23) Critical phenomena in equilibrium statistical mechanics (82B27)

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Elliptic parameterization of Pfaff integrable hierarchies in the zero-dispersion limit ⋮ Dispersionless and multicomponent BKP hierarchies with quantum torus symmetries ⋮ Rank 1 real Wishart spiked model ⋮ DISPERSIONLESS BIGRADED TODA HIERARCHY AND ITS ADDITIONAL SYMMETRY ⋮ The semi-classical limit of Davey-Stewartson hierarchy ⋮ Löwner equations and reductions of dispersionless hierarchies ⋮ Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems ⋮ Bogoyavlensky lattices and generalized Catalan numbers ⋮ Multi-variable reductions of the dispersionless DKP hierarchy ⋮ A note on the extended dispersionless Toda hierarchy ⋮ An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model ⋮ Symmetric matrix ensemble and integrable hydrodynamic chains ⋮ A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary Ensemble ⋮ The Laplace Transform, Mirror Symmetry, and the Topological Recursion of Eynard–Orantin ⋮ A note on reductions of the dispersionless Toda hierarchy

Cites Work

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• Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy
• On universality for orthogonal ensembles of random matrices
• Solitons and infinite dimensional Lie algebras
• Random matrices, graphical enumeration and the continuum limit of Toda lattices
• Duality of real and quaternionic random matrices
• Quantum field theory techniques in graphical enumeration
• Vertex operator solutions to the discrete KP-hierarchy
• Analytic functions and integrable hierarchies -- characterization of tau functions
• Duality of orthogonal and symplectic matrix integrals and quaternionic Feynman graphs
• Dispersionless limit of Hirota equations in some problems of complex analysis
• Pfaff \(\tau\)-functions
• Toda versus Pfaff lattice and related polynomials.
• Integrable structure of the Dirichlet boundary problem in two dimensions
• Asymptotics of unitary and orthogonal matrix integrals
• Orthogonal and Symplectic Matrix Integrals and Coupled KP Hierarchy
• A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves
• Differential Fay identities and auxiliary linear problem of integrable hiearchies
• Second order cumulants of products
• Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices
• On kernel formulas and dispersionless Hirota equations of the extended dispersionless BKP hierarchy
• Hierarchies of Coupled Soliton Equations. I
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• On an Integral Representation for the Genus Series for 2-Cell Embeddings
• Solution of the dispersionless Hirota equations
• On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• The Pfaff lattice on symplectic matrices
• Geometry of the Pfaff Lattices
• Universality in Random Matrix Theory for orthogonal and symplectic ensembles
• On Faber Polynomials
• Conformal maps and integrable hierarchies

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