Toeplitz matrices and Toeplitz determinants under the impetus of the Ising model. Some history and some recent results

Abstract

We review some history and some recent results concerning Toeplitz determinants and their applications. We discuss, in particular, the crucial role of the two-dimensional Ising model in stimulating the development of the theory of Toeplitz determinants.

70 pages, with additions to the text

References in corpus (6)

• Universality for mathematical and physical systems
• Entanglement entropy in quantum spin chains with finite range interaction
• Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
• On the asymptotics of a Toeplitz determinant with singularities
• Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model: II
• Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

Cited by in corpus (7)

• Emptiness formation probability, Toeplitz determinants, and conformal field theory
• On the asymptotics of a Toeplitz determinant with singularities
• The Lattice-Continuum Correspondence in the Ising Model
• Squeezing: from numerical to conceptual problems
• Finite $N$ unitary matrix model
• Sharp asymptotics for Fredholm Pfaffians related to interacting particle systems and random matrices
• Squeezed Fourier Meets Toeplitz Algebras