Browsing by Subject "bordered Toeplitz determinants"

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    Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations
    (arXiv, 2021) Basor, Estelle; Ehrhardt, Torsten; Gharakhloo, Roozbeh; Its, Alexander; Li, Yuqi; Mathematical Sciences, School of Science
    We prove the analogue of the strong Szeg{\H o} limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk \cite{YP} for the next-to-diagonal correlations ⟨σ0,0σN−1,N⟩ in the anisotropic square lattice Ising model, we rigorously justify that the next-to-diagonal long-range order is the same as the diagonal and horizontal ones in the low temperature regime. The anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations is also established. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results.