Browsing by Subject "Riemann-Hilbert approach"

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    The asymptotic behaviour of the discrete holomorphic map Za via the Riemann-Hilbert method
    (Duke, 2016) Bobenko, Alexander I.; Its, Alexander; Department of Mathematical Sciences, School of Science
    We study the asymptotic behavior of the discrete analogue of the holomorphic map zaza. The analysis is based on the use of the Riemann–Hilbert approach. Specifically, using the Deift–Zhou nonlinear steepest descent method we prove the asymptotic formulas which were conjectured in 2000.
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    Riemann–Hilbert approach to a generalized sine kernel
    (Springer Link, 2020-02-01) Gharakhloo, Roozbeh; Its, Alexander R.; Kozlowski, Karol K.; Mathematical Sciences, School of Science
    We derive the large-distance asymptotics of the Fredholm determinant of the so-called generalized sine kernel at the critical point. This kernel corresponds to a generalization of the pure sine kernel arising in the theory of random matrices and has potential applications to the analysis of the large-distance asymptotic behaviour of the so-called emptiness formation probability for various quantum integrable models away from their free fermion point.