Bothner, ThomasDeift, PercyIts, AlexanderKrasovsky, Igor2019-04-122019-04-122018-09Bothner, T., Deift, P., Its, A., & Krasovsky, I. (2018). The sine process under the influence of a varying potential. Journal of Mathematical Physics, 59(9), 091414. https://doi.org/10.1063/1.5050394https://hdl.handle.net/1805/18840We 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.enPublisher PolicyFredholm determinantEuler-Mascheroni constantasymptotic analysisArticle