The sine process under the influence of a varying potential

Thomas Bothner, Percy Deift, Alexander Its, Igor Krasovsky

Research output: Contribution to journalArticle

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 (US)
Article number091414
JournalJournal of Mathematical Physics
Volume59
Issue number9
DOIs
StatePublished - Sep 1 2018

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sin(x+y)
Fredholm Determinant
determinants
Ensemble
Scaling
kernel
scaling
operators
Operator
gases
Model
Review
Influence
Gas

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The sine process under the influence of a varying potential. / Bothner, Thomas; Deift, Percy; Its, Alexander; Krasovsky, Igor.

In: Journal of Mathematical Physics, Vol. 59, No. 9, 091414, 01.09.2018.

Research output: Contribution to journalArticle

Bothner, Thomas ; Deift, Percy ; Its, Alexander ; Krasovsky, Igor. / The sine process under the influence of a varying potential. In: Journal of Mathematical Physics. 2018 ; Vol. 59, No. 9.
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