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arXiv · 1502.04922

Natural Boundary for a Sum Involving Toeplitz Determinants

Craig A. Tracy·Harold Widom
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Abstract

In the theory of the two-dimensional Ising model, the diagonal susceptibility is equal to a sum involving Toeplitz determinants. In terms of a parameter k the diagonal susceptibility is analytic inside the unit circle, and the authors proved the conjecture that this function has the unit circle as a natural boundary. The symbol of the Toepltiz determinants was a k-deformation of one with a single singularity on the unit circle. Here we extend the result, first, to deformations of a larger class of symbols with a single singularity on the unit circle, and then to deformations of (almost) general Fisher-Hartwig symbols.

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Craig A. Tracy, Harold Widom. 2015-02-16. Natural Boundary for a Sum Involving Toeplitz Determinants. https://doi.org/10.1007/978-3-319-49182-0

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