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

Mathematics

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

Abstract

In this paper we continue our analysis [3] of the determinant det(I− γK_s), γ ∈ (0, 1) where Ks is the trace class operator acting in L²(−1, 1) with kernel K_s(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 language	English (US)
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Publisher	Springer International Publishing
Pages	213-234
Number of pages	22
DOIs	https://doi.org/10.1007/978-3-319-49182-0_12
State	Published - 2017

Publication series

Name	Operator Theory: Advances and Applications
Volume	259
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

Access to Document

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

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

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

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

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KW - Riemann-Hilbert problem

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KW - Toeplitz determinant

KW - Transition asymptotics

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On the asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential II

Abstract

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