Semiclassical expansions in the Toda hierarchy and the hermitian matrix model

Abstract

An iterative algorithm for determining a class of solutions of the dispersionful 2-Toda hierarchy characterized by string equations is developed. This class includes the solution which underlies the large N-limit of the Hermitian matrix model in the one-cut case. It is also shown how the double scaling limit can be naturally formulated in this scheme

arXiv comment22 pages

References in corpus (23)

• Integrable Hierarchies and Dispersionless Limit
• Integrable Structure of Interface Dynamics
• Matrix Model Calculations beyond the Spherical Limit
• Conformal maps and dispersionless integrable hierarchies
• Breakdown of universality in multi-cut matrix models
• Normal random matrix ensemble as a growth problem
• Laplacian Growth and Whitham Equations of Soliton Theory
• Vertex operator solutions to the discrete KP-hierarchy
• Dispersionless Toda hierarchy and two-dimensional string theory
• Complex Curve of the Two Matrix Model and its Tau-function
• Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime
• Virasoro Symmetries of the Extended Toda Hierarchy
• Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems
• On Associativity Equations in Dispersionless Integrable Hierarchies
• An alternative approach to KP hierarchy in matrix models
• Higher Genus Correlators from the Hermitian One-Matrix Model
• Bubble break-off in Hele-Shaw flows : Singularities and integrable structures
• Unstable fingering patterns of Hele-Shaw flows as a dispersionless limit of the KdV hierarchy
• Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy
• On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
• Singular limit of Hele-Shaw flow and dispersive regularization of shock waves
• Integrable Discrete Linear Systems and One-Matrix Model
• Genus-zero Whitham hierarchies in conformal-map dynamics

Cited by in corpus (8)

• The multicomponent 2D Toda hierarchy: Discrete flows and string equations
• Partition functions and the continuum limit in Penner matrix models
• The double scaling limit method in the Toda hierarchy
• On the singular sector of the Hermitian random matrix model in the large N limit
• An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model
• Thermodynamic limit of random partitions and dispersionless Toda hierarchy
• An hbar-expansion of the Toda hierarchy: a recursive construction of solutions
• Large N expansions and Painlevé hierarchies in the Hermitian matrix model