Semiclassical orthogonal polynomials, matrix models and isomonodromic tau functions
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Publication:863117
DOI10.1007/s00220-005-1505-4zbMath1131.82306arXivnlin/0410043OpenAlexW2018211673MaRDI QIDQ863117
J. Harnad, Bertrand Eynard, Marco Bertola
Publication date: 25 January 2007
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/nlin/0410043
Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Complex path integral representation for semiclassical linear functionals
- Janossy densities. II: Pfaffian ensembles
- Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems.
- Correlation functions, cluster functions, and spacing distributions for random matrices
- Bilinear semiclassical moment functionals and their integral representation
- On semiclassical linear functionals: Integral representations
- On the linear independence of Laplace integral solutions of certain differential equations
- Partition functions for matrix models and isomonodromic tau functions