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

Research output: Contribution to journal › Article (Academic Journal) › peer-review

9 Citations (Scopus)

122 Downloads (Pure)

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

Access to Document

10.1063/1.5050394

Full-text PDF (author’s accepted manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via American Institute of Physics at https://doi.org/10.1063/1.5050394 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 354 KB

Handle.net

Persistent link

Cite this

@article{7e45ac8fd01f4586895bb2b74040d019,

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.",

author = "Thomas Bothner and Percy Deift and Alexander Its and Igor Krasovsky",

year = "2018",

month = sep,

day = "7",

doi = "10.1063/1.5050394",

language = "English",

volume = "59",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "9",

}

TY - JOUR

T1 - The sine process under the influence of a varying potential

AU - Bothner, Thomas

AU - Deift, Percy

AU - Its, Alexander

AU - Krasovsky, Igor

PY - 2018/9/7

Y1 - 2018/9/7

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.

UR - http://dx.doi.org/10.1063/1.5050394

U2 - 10.1063/1.5050394

DO - 10.1063/1.5050394

M3 - Article (Academic Journal)

SN - 0022-2488

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

Abstract

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this