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Mat. Sb., 2015, Volume 206, Number 1, Pages 103–130 (Mi msb8318)  

This article is cited in 5 scientific papers (total in 5 papers)

On the analogues of Szegő's theorem for ergodic operators

W. Kirsсha, L. Pasturb

a FernUniversität in Hagen
b B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Khar'kov

Abstract: Szegő's theorem on the asymptotic behaviour of the determinants of large Toeplitz matrices is generalized to the class of ergodic operators. The generalization is formulated in terms of a triple consisting of an ergodic operator and two functions, the symbol and the test function. It is shown that in the case of the one-dimensional discrete Schrödinger operator with random ergodic or quasiperiodic potential and various choices of the symbol and the test function this generalization leads to asymptotic formulae which have no analogues in the situation of Toeplitz operators.
Bibliography: 22 titles.

Keywords: Szegő's theorem, random operators, limit theorems.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8318

Full text: PDF file (668 kB)
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English version:
Sbornik: Mathematics, 2015, 206:1, 93–119

Bibliographic databases:

UDC: 517.983.28+519.214+519.216.75
MSC: Primary 47B99; Secondary 35J10, 47B80
Received: 24.12.2013 and 23.07.2014

Citation: W. Kirsсh, L. Pastur, “On the analogues of Szegő's theorem for ergodic operators”, Mat. Sb., 206:1 (2015), 103–130; Sb. Math., 206:1 (2015), 93–119

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Elgart, L. Pastur, M. Shcherbina, “Large block properties of the entanglement entropy of free disordered fermions”, J. Stat. Phys., 166:3-4 (2017), 1092–1127  crossref  mathscinet  zmath  isi  scopus
    2. B. Pfirsch, A. V. Sobolev, “Formulas of Szegő type for the periodic Schrödinger operator”, Commun. Math. Phys., 358:2 (2018), 675–704  crossref  mathscinet  zmath  isi  scopus
    3. A. Dietleine, “Full Szegő-type trace asymptotics for ergodic operators on large boxes”, Commun. Math. Phys., 362:3 (2018), 983–1005  crossref  mathscinet  isi  scopus
    4. F. Nakano, Khanh Duy Trinh, “Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics”, J. Stat. Phys., 173:2 (2018), 295–321  crossref  mathscinet  isi  scopus
    5. L. A. Pastur, M. V. Shcherbina, “Szegő-type theorems for one-dimensional Schrödinger operator with random potential (smooth case)”, Zhurn. matem. fiz., anal., geom., 14:3 (2018), 362–388  mathnet
  • Математический сборник Sbornik: Mathematics (from 1967)
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