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We review some history and some recent results concerning Toeplitz determinants and their applications.
C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen
1907
Earlier work this paper cites.
O. Toeplitz, Zur Transformation der Scharen bilinearer Formen von unendlichvielen Veränderlichen, Nachr. der Kgl. Gessellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse
1907
Earlier work this paper cites.
C. Carathéodory, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen
1911
Earlier work this paper cites.
C. Carathéodory and L. Fejér, Über den Zusammenhang der extremen von harmonishcen Funktionen mit ihren Koeffizienten und über den Picard-Landauschen Satz
1911
Earlier work this paper cites.
O. Toeplitz, Zur Theorie der quadratischen und bilinearen Formen von unendlichvielen Veränderlichen. I. Teil: Theorie der L L -Formen
1911
Earlier work this paper cites.
O. Toeplitz, Zur Theorie der quadratischen und bilinearen Formen von unendlichvielen Veränderlichen
1911
Earlier work this paper cites.
G. Szegő, Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion
1915
Earlier work this paper cites.
G. Szegő, Beiträge zur Theorie der Toeplitzschen Formen, I
1920
Earlier work this paper cites.
G. Szegő, Beiträge zur Theorie der Toeplitzschen Formen, II
1921
Earlier work this paper cites.
E. Ising, Beitrag zur Theorie des Ferromagnetismus
1925
Earlier work this paper cites.
R. Peierls, On Ising’s Model for Ferromagnetism
1936
Earlier work this paper cites.
S. Verblunsky, On positive harmonic functions (second paper)
1936
Earlier work this paper cites.
H. A. Kramers and G. H. Wannier, Statistics of the Two-Dimensional Ferromagnet
1941
Earlier work this paper cites.
B. L. van der Waerden, Die lange Reichweite der regelmässigen Atomanordnung in Mischkristallen
1941
Earlier work this paper cites.
L. Onsager, Crystal Statistics, I. A Two-Dimensional Model with an Order-Disorder Transition
1944
Earlier work this paper cites.
B. Kaufman, Crystal Statistics II. Partition Function Evaluated by Spinor Analysis
1949
Earlier work this paper cites.
B. Kaufman and L. Onsager, Crystal Statistics, III. Short-Range Order in a Binary Ising Lattice
1949
Earlier work this paper cites.
C. H. Chang, The Spontaneous Magnetization of a Two-Dimensional Rectangular Ising Model
1952
Earlier work this paper cites.
M. Kac and J. C. Ward, A combinatorial solution of the two-dimensional Ising model
1952
Earlier work this paper cites.
T. D. Lee and C. N. Yang, Statistical Theory of Equations of State and Phase Transitions II. Lattice Gas and Ising Model
1952
Earlier work this paper cites.
G. Szegő, On certain hermitian forms associated with the Fourier series of a positive function
1952
Earlier work this paper cites.
C. N. Yang, The Spontaneous Magnetization of a Two-Dimensional Ising Model
1952
Earlier work this paper cites.
M. Kac, Toeplitz matrices, translation kernels and a related problem in probability theory
1954
Earlier work this paper cites.
R. B. Potts and J. C. Ward, The Combinatorial Method and the Two-Dimensional Ising Model
1955
Earlier work this paper cites.
B. Gyires, Eigenwerte verallgemeinerter Toeplitzschen Matrizen
1956
Earlier work this paper cites.
E. L. Ince, Ordinary Differential Equations
1956
Earlier work this paper cites.
O. Penrose and L. Onsager, Bose-Einstein condensation and liquid Helium
1956
Earlier work this paper cites.
U. Grenander and G. Szegö, Toeplitz forms and their applications
1958
Earlier work this paper cites.
M. E. Fisher, The susceptibility of the plane Ising model
1959
Earlier work this paper cites.
C. Domb, On the theory of cooperative phenomena in crystals
1960
Earlier work this paper cites.
Ya. L. Geronimus, Polynomials Orthogonal on a Circle and Interval
1960
Earlier work this paper cites.
C. A. Hurst and H. S. Green, New solution of the Ising problem for a rectangular lattice
1960
Earlier work this paper cites.
S. Sherman, Combinatorial aspects of the Ising model for ferromagnetism. I. A conjecture of Feynman on paths and graphs
1960
Earlier work this paper cites.
G. Baxter, A convergence equivalence related to polynomials orthogonal on the unit circle
1961
Earlier work this paper cites.
P. W. Kasteleyn, The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice
1961
Earlier work this paper cites.
H. N. V. Temperley and M. E. Fisher, Dimer problem in statistical mechanics – an exact result
1961
Earlier work this paper cites.
F. Dyson, Statistical theory of the energy levels of complex systems. I
1962
Earlier work this paper cites.
F. Dyson, Statistical theory of the energy levels of complex systems. II
1962
Earlier work this paper cites.
M. E. Fisher, On the theory of critical point density fluctuations
1962
Earlier work this paper cites.
G. Baxter, A norm inequality for a “finite-section” Wiener-Hopf equation
1963
Earlier work this paper cites.
P. N. Burgoyne, Remarks on the combinatorial approach to the Ising problem
1963
Earlier work this paper cites.
F. Dyson, Toeplitz determinants and Coulomb Gases
1963
Earlier work this paper cites.
L. D. Faddeyev, The Inverse Problem in the Quantum Theory of Scattering
1963
Earlier work this paper cites.
P. W. Kasteleyn, Dimer statistics and phase transitions
1963
Earlier work this paper cites.
E. W. Montroll, R. B. Potts, and J. C. Ward, Correlations and Spontaneous Magnetization of the Two-Dimensional Ising Model
1963
Earlier work this paper cites.
T. D. Schultz, Notes on the one-dimensional gas of impenetrable point-particle bosons
1963
Earlier work this paper cites.
R. B. Griffiths, Peierls Proof of Spontaneous Magnetization in a Two-Dimensional Ising Ferromagnet
1964
Earlier work this paper cites.
A. Lenard, Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons
1964
Earlier work this paper cites.
T. D. Schultz, D. C. Mattis, and E. H. Lieb, Two-Dimensional Ising Model as a Soluble Problem of Many Fermions
1964
Earlier work this paper cites.
I. I. Hirschman, Jr., On a theorem of Szegő, Kac, and Baxter
1965
Earlier work this paper cites.
J. M. Myers, Wave scattering and the geometry of a strip
1965
Earlier work this paper cites.
N. V. Vdovichenko, A calculation of the partition function for a plane dipole lattice
1965
Earlier work this paper cites.
H. Widom, Toeplitz matrices in “Studies in Real and Complex Analysis”
1965
Earlier work this paper cites.
M. E. Fisher, On the dimer solution of planar Ising models
1966
Earlier work this paper cites.
L. P. Kadanoff, Spin-Spin Correlations in the Two-Dimensional Ising Model
1966
Earlier work this paper cites.
G. V. Ryazanov, Correlation asymptotics for a Plane Ising Lattice
1966
Earlier work this paper cites.
T. T. Wu, Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. I
1966
Earlier work this paper cites.
H. Cheng and T. T. Wu, Theory of Toeplitz determinants and the spin correlations of the two-dimensional Ising model III
1967
Earlier work this paper cites.
A. Devinatz, The strong Szegő limit theorem
1967
Earlier work this paper cites.
B. M. McCoy and T. T. Wu, Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model, II
1967
Earlier work this paper cites.
M. E. Fisher and R. E. Hartwig, Toeplitz determinants: some applications, theorems and conjectures
1968
Earlier work this paper cites.
I. A. Ibraginov, A theorem of Gabor Szegö
1968
Earlier work this paper cites.
L. A. Sakhnovich, Operators similar to unitary operators
1968
Earlier work this paper cites.
R. E. Hartwig and M. E. Fisher, Asymptotic Behavior of Toeplitz Matrices and Determinants
1969
Earlier work this paper cites.
D. Ruelle, Statistical mechanics
1969
Cited alongside, same era.
G. Gallavotti, Boundary Conditions and Correlation Functions in the ν \nu -Dimensional Ising Model at Low Temperature
1971
Cited alongside, same era.
B. L. Golinskii and I. A. Ibraginov, On Szegö’s limit theorem
1971
Cited alongside, same era.
L. Onsager, The Ising Model in Two-Dimensions, in “Critical Phenomena in Alloys, Magnets, and Superconductors”
1971
Cited alongside, same era.
L. Onsager, Autobiographical Commentary of Lars Onsager, “Critical Phenomena in Alloys, Magnets, and Superconductors”
1971
Cited alongside, same era.
H. Widom, The strong Szegö Limit Theorem for circular arcs
1971
Cited alongside, same era.
E. B. Saff and V. Totik, Logarithmic potentials with external fields
1997
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P. Deift, Orthogonal polynomials and random matrices: A Riemann-Hilbert approach
1998
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R. G. Douglas, Banach Algebra Techniques in Operator Theory
1998
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J. Baik, P. Deift, and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations
1999
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A. Böttcher and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices
1999
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P. Deift, Integrable Operators
1999
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H. Dym and H. P. McKean, Fourier series and integrals
1972
Cited alongside, same era.
J. L. Lebowitz, Bounds on the Correlations and Analyticity Properties of Ferromagnetic Ising Spin Systems
1972
Cited alongside, same era.
J. L. Lebowitz and A. Martin-Löf, On the Uniqueness of the Equilibrium State for Ising Spin Systems
1972
Cited alongside, same era.
A. Lenard, Some remarks on Large Toeplitz determinants
1972
Cited alongside, same era.
G. Benettin, G. Gallavotti, G. Jona-Lasinio, and A. Stella, On the Onsager-Yang-Value of the Spontaneous Magnetization
1973
Cited alongside, same era.
J. W. Helton and R. E. Howe, Integral operators: commutators, traces, index and homology
1973
Cited alongside, same era.
P. Deift, T. Kriecherbauer, K. T-R. McLaughlin, S. Venakides, and X. Zhou, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
1999
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P. Deift, T. Kriecherbauer, K. T-R. McLaughlin, S. Venakides, and X. Zhou, Strong asymptotics of orthogonal polynomials with respect to exponential weights
1999
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B. Nickel, On the singularity structure of the 2D Ising model susceptibility
1999
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E. Basor and H. Widom, On a Toeplitz determinant identity of Borodin and Okounkov
2000
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A. Borodin and A. Okounkov, A Fredholm determinant formula for Toeplitz determinants
2000
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L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics. Vol. 5, Statistical Physics, (Translators: J. B. Sykes, M. J. Kearsley), Butterworth-Heinemann, Oxford (2000)
2000
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B. Nickel, Addendum to: ”On the singularity structure of the 2D Ising model susceptibility”
2000
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H. Au-Yang, B-Q. Jin, and J. H. H. Perk, Wavevector-dependent susceptibility in quasiperiodic Ising models
2001
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T. Ehrhardt, A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities
2001
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A. Its, C. Tracy, and H. Widom, Random words, Toeplitz determinants and integrable systems. II
2001
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E. Wegert, Interpolation by holomorphic functions with restricted boundary values
2001
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D. Bump and P. Diaconis, Toeplitz minors
2002
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V. V. Peller, Hankel Operators and Their Applications
2003
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G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Entanglement in quantum critical phenomena
2003
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B.-Q. Jin and V. E. Korepin, Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
2004
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J. P. Keating and F. Mezzadri, Random Matrix Theory and Entanglement in Quantum Spin Chains
2004
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M. Levitin and E. Shargorodsky, Spectral pollution and second-order relative spectra for self-adjoint operators
2004
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M. L. Mehta, Random matrices
2004
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A. Böttcher and S. M. Grudsky, Spectral Properties of Banded Toeplitz Matrices
2005
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A. Böttcher and H. Widom, Two elementary derivations of the pure Fisher-Hartwig determinant
2005
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F. Francini and A. G. Abanov, Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the X Y XY Spin Chain
2005
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B. Simon, Orthogonal Polynomials on the Unit Circle. Part 1: Classical Theory. Part 2: Spectral Theory
2005
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B. Simon, Trace ideals and their applications
2005
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A. Böttcher and B. Silbermann, Analysis of Toeplitz Operators
2006
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A. Böttcher and H. Widom, Szegő via Jacobi
2006
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A. S. Fokas, A. R. Its, A. A. Kapaev, and V. Yu. Novokshenov, Painlevé Transcendents
2006
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J. P. Keating, Random matrices and number theory
2006
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E. L. Basor and T. Ehrhardt, Asymptotics of block Toeplitz determinants and the classical dimer model
2007
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M. Cafasso, Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies
2007
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P. Deift, Universality for mathematical and physical systems
2007
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P. Deift, A. Its, I. Krasovsky, and X. Zhou, The Widom-Dyson constant for the gap probability in random matrix theory
2007
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S. M. Gonek, C. P. Hughes, and J. P. Keating, A Hybrid Euler-Hadamard product formula for the Riemann zeta function
2007
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A. R. Its, B.-Q. Jin, and V. E. Korepin, Entropy of X Y XY spin chain and block Toeplitz determinants. Universality and renormalization
2007
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I. Lyberg and B. M. McCoy, Form factor expansion of the row and diagonal correlation functions of the two-dimensional Ising model
2007
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J. Palmer, Planar Ising Correlations
2007
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N. S. Witte, Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model
2007
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E. L. Basor and Y. Chen, Toeplitz determinants from compatibility conditions
2008
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H. M. Bui and J. P. Keating, On the mean values of L L -functions in orthogonal and symplectic families
2008
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P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral
2008
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A. R. Its, F. Mezzadri, and M. Y. Mo, Entanglement entropy in quantum spin chains with finite range interaction
2008
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H. Widom, Asymptotics of a class of operator determinants with application to the cylindrical Toda equations
2008
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A. R. Its and V. E. Korepin, The Fisher-Hartwig Formula and Entanglement Entropy
2009
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D. Niles, The Riemann-Hilbert -Birkhoff inverse monodromy problem and connection formulae for the third Painlevé transcendent
2009
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A. A. Ovchinnikov, Fisher-Hartwig conjecture and the correlators in the impenetrable Bose gas
2009
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A. Böttcher, S. M. Grudsky, and E. A. Maksimenko, Inside the eigenvalues of certain Hermitian Toeplitz band matrices
2010
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M. Duits, K. Johansson, Powers of large random unitary matrices and Toeplitz determinants
2010
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M. Levitin, A. V. Sobolev, and D. Sobolev, On the near periodicity of eigenvalues of Toeplitz matrices
2010
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R. J. Baxter, Onsager and Kaufman’s calculation of the spontaneous magnetization of the Ising model
2011
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T. Claeys, A. Its, and I. Krasovsky, Emergence of a singularity for Toeplitz determinants and Painlevé V
2011
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P. Deift, A. Its, and I. Krasovsky, Asymptotics of Toeplitz, Hankel and Toeplitz+Hankel Determinants with Fisher-Hartwig Singularities
2011
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D. B. Gutman, Y. Gefen, and A. D. Mirlin, Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
2011
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I. Krasovsky, Aspects of Toeplitz determinants
2011
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B. M. McCoy, The Romance of the Ising Model
2011
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H. Pinson, Rotational Invariance of the 2d Spin Spin Correlation Function
2011
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P. Deift, A. Its, and I. Krasovsky, Eigenvalues of Toeplitz matrices in the bulk of the spectrum
2012
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C. N. Yang, Selected Papers 1945–1980 with Commentary
2012
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P. J. Forrester and N. E. Frankel, Applications and generalizations of Fisher-Hartwig asymptotics
2028
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