Browsing by Subject "Fredholm determinant"

Now showing 1 - 3 of 3
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    Large-x analysis of an operator valued Riemann–Hilbert problem
    (Oxford, 2016) Its, Alexander R.; Kozlowski, K. K.; Department of Mathematical Sciences, School of Science
    The purpose of this paper is to push forward the theory of operator-valued Riemann–Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method á la Deift–Zhou. In this paper, we demonstrate that the operator-valued Riemann–Hilbert problem arising in the characterization of so-called cc-shifted integrable integral operators allows one to extract the large-xx asymptotics of the Fredholm determinant associated with such operators.
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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.
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    The sine process under the influence of a varying potential
    (AIP, 2018-09) Bothner, Thomas; Deift, Percy; Its, Alexander; Krasovsky, Igor; Mathematical Sciences, School of Science
    We review the authors’ recent work where we obtain the uniform large s asymptotics for the Fredholm determinant D(s,γ)≔det(I−γKs↾L2(−1,1)), 0 ≤ γ ≤ 1. The operator Ks acts with kernel Ks(x, y) = sin(s(x − y))/(π(x − y)), and D(s, γ) appears for instance in Dyson’s model of a Coulomb log-gas with varying external potential or in the bulk scaling analysis of the thinned Gaussian unitary ensemble.