Asymptotics and integrable structures for biorthogonal polynomials associated to a random two-matrix model

DOI10.1016/S0167-2789(01)00173-7zbMath1038.82042OpenAlexW1971402037MaRDI QIDQ5940212

Nicholas M. Ercolani, Kenneth T.-R. McLaughlin

Publication date: 2001

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(01)00173-7

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52) Other special functions (33E99) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items

The Hermitian two matrix model with an even quartic potential, Bilinear semiclassical moment functionals and their integral representation, Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials, Interlacing properties of roots of certain biorthogonal polynomials, A critical phenomenon in the two-matrix model in the quartic/quadratic case, Biorthogonal polynomials for two-matrix models with semiclassical potentials, New algebraic structures from Hermitian one-matrix model, Lusztig factorization dynamics of the full Kostant-Toda lattices, On the relation between the full Kostant-Toda lattice and multiple orthogonal polynomials, Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials, Orthogonal polynomials in the normal matrix model with a cubic potential, Large \(N\) expansion of the 2-matrix model, Painlevé kernels in Hermitian matrix models, A Riemann-Hilbert problem for skew-orthogonal polynomials, Cauchy biorthogonal polynomials, A Riemann-Hilbert problem for biorthogonal polynomials, Generalizations of orthogonal polynomials, Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients, Universality in the two matrix model with a monomial quartic and a general even polynomial potential, Average characteristic polynomials in the two-matrix model

Cites Work

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• Quantum field theory techniques in graphical enumeration
• A method of integration over matrix variables
• On Whittaker vectors and representation theory
• The spectrum of coupled random matrices
• Fredholm determinants, differential equations and matrix models
• Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices
• On the statistical mechanics approach in the random matrix theory: Integrated density of states.
• Correlation functions, cluster functions, and spacing distributions for random matrices
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• Toda flows with infinitely many variables
• Planar diagrams
• On the density of Eigenvalues of a random matrix
• Sur la loi limite de l'espacement des valeurs propres d'une matrice ale´atoire
• On the distribution of the length of the longest increasing subsequence of random permutations
• A continuum limit of the Toda lattice
• COMBINATORICS OF THE MODULAR GROUP II THE KONTSEVICH INTEGRALS
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory