Details

Autor(en) / Beteiligte

• Bothner, Thomas
• Deift, Percy
• Its, Alexander
• Krasovsky, Igor
• Ehrhardt, Torsten
• Bini, Dario A.
• Karlovich, Alexei Yu
• Spitkovsky, Ilya

Titel

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

Ist Teil von

• Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics, 2017, Vol.259, p.213-234

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2017

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper we continue our analysis [3] of the determinant det\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ ({I}- {\gamma}{K}_{s}), \ {\gamma} \ {\in} \ (0, 1)$$ \end{document} where Ks is the trace class operator acting in L2(−1, 1) with kernel \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $${K}_{s}(\lambda, \mu) = \frac{{\rm{sin}} \ {s}(\lambda-\mu)}{{\pi}(\lambda-\mu)}$$ \end{document}. 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).