The sine process under the influence of a varying potential

Thomas Bothner; Percy Deift; Alexander Its; Igor Krasovsky

doi:10.1063/1.5050394

The sine process under the influence of a varying potential

Thomas Bothner, Percy Deift, Alexander Its, Igor Krasovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

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 K_s acts with kernel K_s(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 language	English (US)
Article number	091414
Journal	Journal of Mathematical Physics
Volume	59
Issue number	9
DOIs	https://doi.org/10.1063/1.5050394
State	Published - Sep 1 2018

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.5050394

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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.",

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The sine process under the influence of a varying potential

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