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

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this paper we continue our analysis [3] of the determinant det(I− γKs), γ ∈ (0, 1) where Ks is the trace class operator acting in L2(−1, 1) with kernel Ks(λ, μ) = (Formula Present). 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 languageEnglish (US)
Title of host publicationOperator Theory: Advances and Applications
PublisherSpringer International Publishing
Pages213-234
Number of pages22
Volume259
DOIs
StatePublished - 2017

Publication series

NameOperator Theory: Advances and Applications
Volume259
ISSN (Print)02550156
ISSN (Electronic)22964878

Fingerprint

Scaling Limit
Asymptotic Behavior
Trace Class Operators
Proposition
Determinant
Continue
kernel
Theorem
Gas

Keywords

  • Deift-Zhou nonlinear steepest descent method
  • Riemann-Hilbert problem
  • Sine kernel determinant
  • Toeplitz determinant
  • Transition asymptotics

ASJC Scopus subject areas

  • Analysis

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 Operator Theory: Advances and Applications (Vol. 259, pp. 213-234). (Operator Theory: Advances and Applications; Vol. 259). Springer International Publishing. 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; Krasovsky, Igor.

Operator Theory: Advances and Applications. Vol. 259 Springer International Publishing, 2017. p. 213-234 (Operator Theory: Advances and Applications; Vol. 259).

Research output: Chapter in Book/Report/Conference proceedingChapter

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 Operator Theory: Advances and Applications. vol. 259, Operator Theory: Advances and Applications, vol. 259, Springer International Publishing, pp. 213-234. https://doi.org/10.1007/978-3-319-49182-0_12
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 Operator Theory: Advances and Applications. Vol. 259. Springer International Publishing. 2017. p. 213-234. (Operator Theory: Advances and Applications). https://doi.org/10.1007/978-3-319-49182-0_12
Bothner, Thomas ; Deift, Percy ; Its, Alexander ; Krasovsky, Igor. / On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II. Operator Theory: Advances and Applications. Vol. 259 Springer International Publishing, 2017. pp. 213-234 (Operator Theory: Advances and Applications).
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