|
This article is cited in 7 scientific papers (total in 7 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)
References:
PDF file
HTML file
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
\Bibitem{KirPas15}
\by W.~Kirsсh, L.~Pastur
\paper On the analogues of Szeg\H{o}'s theorem for ergodic operators
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 1
\pages 103--130
\mathnet{http://mi.mathnet.ru/msb8318}
\crossref{https://doi.org/10.4213/sm8318}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3354964}
\zmath{https://zbmath.org/?q=an:06439410}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2015SbMat.206...93K}
\elib{https://elibrary.ru/item.asp?id=23421600}
\transl
\jour Sb. Math.
\yr 2015
\vol 206
\issue 1
\pages 93--119
\crossref{https://doi.org/10.1070/SM2015v206n01ABEH004448}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000351527000007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925277805}
Linking options:
http://mi.mathnet.ru/eng/msb8318https://doi.org/10.4213/sm8318 http://mi.mathnet.ru/eng/msb/v206/i1/p103
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
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
-
B. Pfirsch, A. V. Sobolev, “Formulas of Szegő type for the periodic Schrödinger operator”, Commun. Math. Phys., 358:2 (2018), 675–704
-
A. Dietleine, “Full Szegő-type trace asymptotics for ergodic operators on large boxes”, Commun. Math. Phys., 362:3 (2018), 983–1005
-
F. Nakano, Khanh Duy Trinh, “Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics”, J. Stat. Phys., 173:2 (2018), 295–321
-
L. Pastur, M. Shcherbina, “Szegö-type theorems for one-dimensional Schrödinger operator with random potential (smooth case)”, Zhurn. matem. fiz., anal., geom., 14:3 (2018), 362–388
 -
von Soosten P., Warzel S., “Delocalization and Continuous Spectrum For Ultrametric Random Operators”, Ann. Henri Poincare, 20:9 (2019), 2877–2898
-
Kutsenko A.A., “Matrix Representations of Multidimensional Integral and Ergodic Operators”, Appl. Math. Comput., 369 (2020), 124818
|
| Number of views: |
| This page: | 348 | | Full text: | 98 | | References: | 54 | | First page: | 36 |
|
Terms of Use