On the finite-gap ansatz in the continuum limit of the Toda lattice

DOI10.1215/S0012-7094-00-10434-6zbMath0966.37037OpenAlexW1983218727MaRDI QIDQ1586405

Arno B. J. Kuijlaars

Publication date: 14 August 2001

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-00-10434-6

zbMATH Keywords

orthogonal polynomialsToda latticeextremal problem

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) Lattice dynamics; integrable lattice equations (37K60)

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A numerical solution of the constrained energy problem ⋮ Nonintersecting Brownian motions on the unit circle ⋮ Precise deviations for discrete ensembles ⋮ Dubrovin method and the Toda chain ⋮ Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions ⋮ Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions: Antiferroelectric Phase ⋮ Constrained Leja points and the numerical solution of the constrained energy problem ⋮ Green equilibrium measures and representations of an external field ⋮ Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients ⋮ Thermodynamics of the six-vertex model in an L-shaped domain

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