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
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Pages213-234
Number of pages22
DOIs
StatePublished - 2017

Publication series

NameOperator Theory: Advances and Applications
Volume259
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

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

ASJC Scopus subject areas

  • Analysis

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  • 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 (pp. 213-234). (Operator Theory: Advances and Applications; Vol. 259). Springer International Publishing. https://doi.org/10.1007/978-3-319-49182-0_12