The Onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators.

DOI10.1007/BF02183366zbMath1080.47502OpenAlexW252959283WikidataQ122919194 ScholiaQ122919194MaRDI QIDQ1593178

Albrecht Böttcher

Publication date: 16 January 2001

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02183366

zbMATH Keywords

Ising modelcorrelation functionsToeplitz operatorsToeplitz determinantsspontaneous magnetizationSzegö limit theorems

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35)

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The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities ⋮ Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results ⋮ Asymptotics of determinants with a rotation-invariant weight and discontinuities along circles ⋮ Uniform asymptotics of Toeplitz determinants with Fisher-Hartwig singularities ⋮ An operator theoretic approach to the brickwork Ising model with second-neighbor interactions ⋮ The generalised Dyson circular unitary ensemble: asymptotic distribution of the eigenvalues at the origin of the spectrum ⋮ Crossing bridges with strong Szegő limit theorem ⋮ More Than 40 Years of Algebraic Techniques in Numerical Analysis

Cites Work

• Toeplitz matrices and determinants with Fisher-Hartwig symbols
• Asymptotic behavior of block Toeplitz matrices and determinants. II
• A continuous analogue of the Fisher-Hartwig formula for piecewise continuous symbols
• Toeplitz matrices, translation kernels and a related problem in probability theory
• The asymptotic behavior of Toeplitz determinants for generating functions with zeros of integral orders
• Lokale Theorie des Reduktionsverfahrens für Toeplitzoperatoren
• Asymptotic Formulas for Toeplitz Determinants
• Toeplitz Operators and Determinants Generated by Symbols with One Fisher-Hartwig Singularity
• Toeplitz Determinants with Singular Generating Functions
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