@article{623aebd5cdc743208816b8345695a2da,
title = "The sine process under the influence of a varying potential",
abstract = "We review the authors{\textquoteright} 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{\textquoteright}s model of a Coulomb log-gas with varying external potential or in the bulk scaling analysis of the thinned Gaussian unitary ensemble.",
author = "Thomas Bothner and Percy Deift and Alexander Its and Igor Krasovsky",
note = "Funding Information: T.B. acknowledges support of the AMS and the Simons Foundation through a travel grant. The work of P.D. is supported under NSF Grant No. DMS-1300965, and A.I. acknowledges support of the NSF Grant No. DMS-1700261 and the Russian Science Foundation Grant No. 17-11-01126. I.K.{\textquoteright}s work is supported by the Leverhulme Trust research project Grant No. RPG-2018-260. Publisher Copyright: {\textcopyright} 2018 Author(s).",
year = "2018",
month = sep,
day = "1",
doi = "10.1063/1.5050394",
language = "English (US)",
volume = "59",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "9",
}