Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics [book]

Dario A. Bini, Torsten Ehrhardt, Alexei Yu. Karlovich, Ilya Spitkovsky
2017 Operator Theory: Advances and Applications  
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
more » ... of symbols with a single singularity on the unit circle, and then to deformations of (almost) general Fisher-Hartwig symbols.
doi:10.1007/978-3-319-49182-0 fatcat:hj7fa4ulm5hynlt2zsdaszv3ba