The sine process under the influence of a varying potential

Thomas Bothner*, Percy Deift, Alexander Its, Igor Krasovsky

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

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.
Original languageEnglish
Article number091414
JournalJournal of Mathematical Physics
Volume59
Issue number9
Early online date7 Sep 2018
DOIs
Publication statusE-pub ahead of print - 7 Sep 2018

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