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

^*Corresponding author for this work

School of Mathematics

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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 language	English
Article number	091414
Journal	Journal of Mathematical Physics
Volume	59
Issue number	9
Early online date	7 Sept 2018
DOIs	https://doi.org/10.1063/1.5050394
Publication status	E-pub ahead of print - 7 Sept 2018

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title = "The sine process under the influence of a varying potential",

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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AU - Bothner, Thomas

AU - Deift, Percy

AU - Its, Alexander

AU - Krasovsky, Igor

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N2 - 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.

AB - 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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U2 - 10.1063/1.5050394

DO - 10.1063/1.5050394

M3 - Article (Academic Journal)

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VL - 59

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 9

M1 - 091414

ER -

The sine process under the influence of a varying potential

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