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Zh. Mat. Fiz. Anal. Geom., 2008, Volume 4, Number 1, Pages 7–23 (Mi jmag82)  

This article is cited in 4 scientific papers (total in 4 papers)

Distance matrices and isometric embeddings

E. Bohomolny, O. Bohigas, C. Schmit

Université Patis-Sud, CNRS, UMR 8626, Laboratoire de Physique Théorique et Modèles Statistiques, 91405 Orsay Cedex, France

Abstract: We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one nonpositive. Several generalizations are discussed.

Key words and phrases: Anderson model, localization, Wegner estimate.

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Bibliographic databases:
MSC: 15A52, 82B41
Received: 10.10.2007
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Citation: E. Bohomolny, O. Bohigas, C. Schmit, “Distance matrices and isometric embeddings”, Zh. Mat. Fiz. Anal. Geom., 4:1 (2008), 7–23

Citation in format AMSBIB
\Bibitem{BohBohSch08}
\by E.~Bohomolny, O.~Bohigas, C.~Schmit
\paper Distance matrices and isometric embeddings
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2008
\vol 4
\issue 1
\pages 7--23
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2404171}
\zmath{https://zbmath.org/?q=an:1151.82016}
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\elib{http://elibrary.ru/item.asp?id=12834747}


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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. Zeng X., “Distributions For the Eigenvalues of Large Random Matrices Generated From Four Manifolds”, J. Phys. A-Math. Theor., 47:2 (2014), 025206  crossref  zmath  isi  scopus
    2. Jiang T., “Distributions of Eigenvalues of Large Euclidean Matrices Generated From l(P) Balls and Spheres”, Linear Alg. Appl., 473:SI (2015), 14–36  crossref  zmath  isi  scopus
    3. Christophe F., Laukkarinen T., Mikkonen T., Massera J., Andalibi V., “Building Wireless Sensor Networks With Biological Cultures: Components and Integration Challenges”, Int. J. Parallel Emerg. Distrib. Syst., 32:1, SI (2017), 56–73  crossref  isi  scopus
    4. Hermi L., Saito N., “On Rayleigh-Type Formulas For a Non-Local Boundary Value Problem Associated With An Integral Operator Commuting With the Laplacian”, Appl. Comput. Harmon. Anal., 45:1 (2018), 59–83  crossref  zmath  isi  scopus
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