The sine process under the influence of a varying potential

Thomas Bothner, Percy Deift, Alexander Its, Igor Krasovsky

Research output: Contribution to journalArticlepeer-review


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 (US)
Article number091414
JournalJournal of Mathematical Physics
Issue number9
StatePublished - Sep 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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