Browsing by Subject "asymptotic analysis"

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    A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants
    (SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 2020-10-06) Gharakhloo, Roozbeh; Its, Alexander; Mathematical Sciences, School of Science
    In this paper we will formulate 4×4 Riemann-Hilbert problems for Toeplitz+Hankel determinants and the associated system of orthogonal polynomials, when the Hankel symbol is supported on the unit circle and also when it is supported on an interval [a,b], 0
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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.