2017 | OriginalPaper | Chapter
Natural Boundary for a Sum Involving Toeplitz Determinants
Authors : Craig A. Tracy, Harold Widom
Published in: Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
Publisher: Springer International Publishing
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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 for |k| < 1, 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.