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The sine process under the influence of a varying potential

Research output: Contribution to journalArticle

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

Original languageEnglish
JournalJOURNAL OF MATHEMATICAL PHYSICS
Volume59
Early online date7 Sep 2018
DOIs
Accepted/In pressAug 2018
E-pub ahead of print7 Sep 2018

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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.

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