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

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arxiv 1207.4990 v3 pith:7XUKGHJC submitted 2012-07-20 math.FA math-phmath.CAmath.MP

P. Deift , A. Its , I. Krasovsky This is my paper · ORCID
classification math.FAmath-phmath.CAmath.MP
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants

    math-ph 2019-09 accept novelty 8.0 of 10

    A 4x4 Riemann-Hilbert formalism gives large-n asymptotics for Toeplitz+Hankel determinants with independent symbols, conditional on a non-degeneracy bound and verified for an explicit family.

  2. Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution

    math-ph 2026-03 conditional novelty 7.0 of 10

    The full persistence distribution in 1D Ising coarsening equals a Pfaffian Fredholm determinant of the sech kernel and is controlled by a Painlevé VI equation that is the mean curvature of a Bonnet surface.

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