Toda versus Pfaff lattice and related polynomials.
From MaRDI portal
Publication:1847905
DOI10.1215/S0012-9074-02-11211-3zbMath1067.37111OpenAlexW2054140086MaRDI QIDQ1847905
Pierre van Moerbeke, Mark Adler
Publication date: 27 October 2002
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1215/s0012-9074-02-11211-3
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Lattice dynamics; integrable lattice equations (37K60) Exactly solvable dynamic models in time-dependent statistical mechanics (82C23)
Related Items
Integrable lattice hierarchies behind Cauchy two-matrix model and Bures ensemble, Partial-skew-orthogonal polynomials and related integrable lattices with Pfaffian tau-functions, Finite dimensional integrable systems related to two dimensional \(A^{(2)}_{2l},C_{l}^{(1)}\) and \(D_{l+1}^{(2)}\) Toda equations, Tau-function theory of chaotic quantum transport with \(\beta = 1, 2, 4\), Pfaffian decomposition and a Pfaffian analogue of \(q\)-Catalan Hankel determinants, Pfaffian and determinantal tau functions, Gaussian multiplicative chaos for Gaussian orthogonal and symplectic ensembles, Christoffel transformations for (partial-)skew-orthogonal polynomials and applications, Asymptotic expansion of matrix models in the multi-cut regime, Linear problems and Bäcklund transformations for the Hirota-Ohta system, Tracy-Widom distributions for the Gaussian orthogonal and symplectic ensembles revisited: a skew-orthogonal polynomials approach, Unnamed Item, On the proof of universality for orthogonal and symplectic ensembles in random matrix theory, Universality for orthogonal and symplectic Laguerre-type ensembles, Darboux transformations and exact solutions of two dimensional A2n(2) Toda equation, A Riemann-Hilbert problem for skew-orthogonal polynomials, Fifty years of the finite nonperiodic Toda lattice: a geometric and topological viewpoint, Symmetric matrix ensemble and integrable hydrodynamic chains, The partition function of the Bures ensemble as theτ-function of BKP and DKP hierarchies: continuous and discrete, A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary Ensemble, Dressing method and the coupled KP hierarchy, Combinatorics of dispersionless integrable systems and universality in random matrix theory, The AKS theorem, A.C.I. systems and random matrix theory, Moments of the transmission eigenvalues, proper delay times, and random matrix theory. I
Cites Work
- Completely integrable systems, Euclidean Lie algebras, and curves
- Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
- Classical skew orthogonal polynomials and random matrices
- Pfaff \(\tau\)-functions
- A Lax representation for the vertex operator and the central extension
- Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials
- Matrix Integrals and the Geometry of Spinors
- Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum.
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
