The correspondence between Tracy–Widom and Adler–Shiota–van Moerbeke approaches in random matrix theory: The Gaussian case

DOI10.1063/1.2890428zbMath1152.81596arXiv0712.0862OpenAlexW3106317405MaRDI QIDQ5504880

Igor Rumanov

Publication date: 23 January 2009

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

Full work available at URL: https://arxiv.org/abs/0712.0862

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Percolation (82B43) Probability theory on linear topological spaces (60B11)

Related Items (3)

A centerless representation of the Virasoro algebra associated with the unitary circular ensemble ⋮ A PDE for the multi-time joint probability of the Airy process ⋮ Universal structure and universal equations (PDE) for unitary ensembles

Cites Work

• Differential equations for Dyson processes
• The spectrum of coupled random matrices
• Level-spacing distributions and the Airy kernel
• Fredholm determinants, differential equations and matrix models
• Collective field theory, Calogero-Sutherland model and generalized matrix models
• Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems.
• Duality, biorthogonal polynomials and multi-matrix models
• Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• The Jacobi polynomial ensemble and the Painlevé VI equation
• On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices
• DIFFERENTIAL EQUATIONS FOR QUANTUM CORRELATION FUNCTIONS
• Radiation loss of dispersion-managed solitons in optical fibers
• Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum.

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