On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II

Thomas Bothner; Percy Deift; Alexander  Its; Igor Krasovsky

doi:10.1007/978-3-319-49182-0_12

On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II

Thomas Bothner, Percy Deift, Alexander Its, Igor Krasovsky

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

11 Citations (Scopus)

2 Downloads (Pure)

Abstract

In this paper we continue our analysis [3] of the determinant det (I−γKs), γ ∈ (0,1) where K s is the trace class operator acting in L 2(−1, 1) with kernel Ks(λ,μ)=sin s(λ−μ)π(λ−μ) . In [3] various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below).

Original language	English
Title of host publication	Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics
Subtitle of host publication	The Albrecht Böttcher Anniversary Volume
Editors	Dario A. Bini, Torsten Ehrhardt, Alexei Yu. Karlovich, Ilya Spitkovsky
Publisher	Springer
Pages	213-234
Volume	259
ISBN (Electronic)	9783319491820
ISBN (Print)	9783319491806, 9783319840970
DOIs	https://doi.org/10.1007/978-3-319-49182-0_12
Publication status	E-pub ahead of print - 23 Mar 2017

Publication series

Name	Operator Theory: Advances and Applications
Publisher	Springer
Volume	259
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Access to Document

10.1007/978-3-319-49182-0_12

Full-text PDF (accepted manuscript)
This is the accepted author manuscript (AAM). The final published version (Version of Record) can be found on the publisher's website. The copyright of any third-party content, such as images, remains with the copyright holder.
Accepted author manuscript, 642 KBLicence: Unspecified

Handle.net

Persistent link

Cite this

Bothner, T., Deift, P., Its, A., & Krasovsky, I. (2017). On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II. In D. A. Bini, T. Ehrhardt, A. Y. Karlovich, & I. Spitkovsky (Eds.), Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: The Albrecht Böttcher Anniversary Volume (Vol. 259, pp. 213-234). ( Operator Theory: Advances and Applications; Vol. 259). Springer. Advance online publication. https://doi.org/10.1007/978-3-319-49182-0_12

Bothner, Thomas ; Deift, Percy ; Its, Alexander et al. / On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II. Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: The Albrecht Böttcher Anniversary Volume. editor / Dario A. Bini ; Torsten Ehrhardt ; Alexei Yu. Karlovich ; Ilya Spitkovsky. Vol. 259 Springer, 2017. pp. 213-234 ( Operator Theory: Advances and Applications).

@inbook{db91a33f51fb402987552069124404d2,

title = "On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II",

abstract = "In this paper we continue our analysis [3] of the determinant det (I−γKs), γ ∈ (0,1) where K s is the trace class operator acting in L 2(−1, 1) with kernel Ks(λ,μ)=sin s(λ−μ)π(λ−μ) . In [3] various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below).",

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

year = "2017",

month = mar,

day = "23",

doi = "10.1007/978-3-319-49182-0_12",

language = "English",

isbn = "9783319491806",

volume = "259",

series = " Operator Theory: Advances and Applications",

publisher = "Springer",

pages = "213--234",

editor = "Bini, {Dario A.} and Torsten Ehrhardt and Karlovich, { Alexei Yu.} and Ilya Spitkovsky",

booktitle = "Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics",

}

Bothner, T, Deift, P, Its, A & Krasovsky, I 2017, On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II. in DA Bini, T Ehrhardt, AY Karlovich & I Spitkovsky (eds), Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: The Albrecht Böttcher Anniversary Volume. vol. 259, Operator Theory: Advances and Applications, vol. 259, Springer, pp. 213-234. https://doi.org/10.1007/978-3-319-49182-0_12

On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II. / Bothner, Thomas; Deift, Percy; Its, Alexander et al.
Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: The Albrecht Böttcher Anniversary Volume. ed. / Dario A. Bini; Torsten Ehrhardt; Alexei Yu. Karlovich; Ilya Spitkovsky. Vol. 259 Springer, 2017. p. 213-234 ( Operator Theory: Advances and Applications; Vol. 259).

Research output: Chapter in Book/Report/Conference proceeding › Chapter in a book

TY - CHAP

T1 - On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II

AU - Bothner, Thomas

AU - Deift, Percy

AU - Its, Alexander

AU - Krasovsky, Igor

PY - 2017/3/23

Y1 - 2017/3/23

N2 - In this paper we continue our analysis [3] of the determinant det (I−γKs), γ ∈ (0,1) where K s is the trace class operator acting in L 2(−1, 1) with kernel Ks(λ,μ)=sin s(λ−μ)π(λ−μ) . In [3] various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below).

AB - In this paper we continue our analysis [3] of the determinant det (I−γKs), γ ∈ (0,1) where K s is the trace class operator acting in L 2(−1, 1) with kernel Ks(λ,μ)=sin s(λ−μ)π(λ−μ) . In [3] various key asymptotic results were stated and utilized, but without proof: Here we provide the proofs (see Theorem 1.2 and Proposition 1.3 below).

U2 - 10.1007/978-3-319-49182-0_12

DO - 10.1007/978-3-319-49182-0_12

M3 - Chapter in a book

SN - 9783319491806

SN - 9783319840970

VL - 259

T3 - Operator Theory: Advances and Applications

SP - 213

EP - 234

BT - Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics

A2 - Bini, Dario A.

A2 - Ehrhardt, Torsten

A2 - Karlovich, Alexei Yu.

A2 - Spitkovsky, Ilya

PB - Springer

ER -

Bothner T, Deift P, Its A, Krasovsky I. On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II. In Bini DA, Ehrhardt T, Karlovich AY, Spitkovsky I, editors, Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics: The Albrecht Böttcher Anniversary Volume. Vol. 259. Springer. 2017. p. 213-234. ( Operator Theory: Advances and Applications). Epub 2017 Mar 23. doi: 10.1007/978-3-319-49182-0_12

On the Asymptotic Behavior of a Log Gas in the Bulk Scaling Limit in the Presence of a Varying External Potential II

Abstract

Publication series

Access to Document

Handle.net

Fingerprint

Cite this