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Zap. Nauchn. Sem. POMI, 2007, Volume 341, Pages 68–80 (Mi znsl134)  

This article is cited in 3 scientific papers (total in 3 papers)

Limit correlation functions at zero for fixed trace random matrix ensembles

F. Götzea, M. I. Gordinb, A. Levinac

a Bielefeld University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
c Max Planck Institute for Dynamics and Self-Organization

Abstract: The large-$N$ limit of the eigenvalue correlation functions is examined in a neighborhood of zero for the spectra of $N\times N-$Hermitian matrices chosen at random from the Hilbert–Schmidt sphere of appropriate radius. Dyson's famous $\sin\pi(t_1-t_2)/\pi(t_1-t_2)$-kernel asymptotics is extended to this class of random matrix ensembles.

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English version:
Journal of Mathematical Sciences (New York), 2007, 147:4, 6884–6890

Bibliographic databases:

UDC: 519.2
Received: 29.03.2007

Citation: F. Götze, M. I. Gordin, A. Levina, “Limit correlation functions at zero for fixed trace random matrix ensembles”, Probability and statistics. Part 11, Zap. Nauchn. Sem. POMI, 341, POMI, St. Petersburg, 2007, 68–80; J. Math. Sci. (N. Y.), 147:4 (2007), 6884–6890

Citation in format AMSBIB
\Bibitem{GotGorLev07}
\by F.~G\"otze, M.~I.~Gordin, A.~Levina
\paper Limit correlation functions at zero for fixed trace random matrix ensembles
\inbook Probability and statistics. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 341
\pages 68--80
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2363585}
\zmath{https://zbmath.org/?q=an:1153.60026}
\elib{http://elibrary.ru/item.asp?id=9593761}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 147
\issue 4
\pages 6884--6890
\crossref{https://doi.org/10.1007/s10958-007-0511-9}
\elib{http://elibrary.ru/item.asp?id=13544165}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36048930161}


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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. Götze F., Gordin M., “Limit correlation functions for fixed trace random matrix ensembles”, Commun. Math. Phys., 281:1 (2008), 203–229  crossref  zmath  adsnasa  isi  elib  scopus
    2. Zhou Da-Sheng, Liu Dang-Zheng, Qian Tao, “Fixed trace $\beta$-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density”, J. Math. Phys., 51:3 (2010), 033301, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Liu D.-Zh., Zhou D.-Sh., “Local statistical properties of Schmidt eigenvalues of bipartite entanglement for a random pure state”, Int. Math. Res. Not. IMRN, 2011, no. 4, 725–766  mathscinet  zmath  isi
  • Записки научных семинаров ПОМИ
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