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Mosc. Math. J., 2014, Volume 14, Number 1, Pages 29–38 (Mi mmj513)  

This article is cited in 10 scientific papers (total in 10 papers)

CLT for spectra of submatrices of Wigner random matrices

Alexei Borodinab

a IITP RAS, Bolshoy Karetny per. 19, Moscow, 127994, Russia
b Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139, USA

Abstract: We prove a CLT for spectra of submatrices of real symmetric and Hermitian Wigner matrices. We show that if in the standard normalization the fourth moment of the off-diagonal entries is GOE/GUE-like then the limiting Gaussian process can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields.

Key words and phrases: Wigner random matrix, Gaussian fluctuations, Gaussian Free Field.

DOI: https://doi.org/10.17323/1609-4514-2014-14-1-29-38

Full text: http://www.mathjournals.org/.../2014-014-001-002.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 60B20, 60G15
Received: October 5, 2010; in revised form June 15, 2013
Language:

Citation: Alexei Borodin, “CLT for spectra of submatrices of Wigner random matrices”, Mosc. Math. J., 14:1 (2014), 29–38

Citation in format AMSBIB
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\by Alexei~Borodin
\paper CLT for spectra of submatrices of Wigner random matrices
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 1
\pages 29--38
\mathnet{http://mi.mathnet.ru/mmj513}
\crossref{https://doi.org/10.17323/1609-4514-2014-14-1-29-38}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3221945}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789200002}


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    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:
    1. A. Borodin, “CLT for spectra of submatrices of Wigner random matrices, II: Stochastic evolution”, Random matrix theory, interacting particle systems, and integrable systems, Math. Sci. Res. Inst. Publ., 65, Cambridge Univ. Press, New York, 2014, 57–69  mathscinet  zmath  isi
    2. A. Borodin, V. Gorin, “General $\beta$-Jacobi corners process and the Gaussian free field”, Commun. Pure Appl. Math., 68:10 (2015), 1774–1844  crossref  zmath  isi  elib  scopus
    3. A. Borodin, I. Corwin, V. Gorin, “Stochastic six-vertex model”, Duke Math. J., 165:3 (2016), 563–624  crossref  zmath  isi  elib  scopus
    4. I.-J Jeong., S. Sodin, “A limit theorem for stochastically decaying partitions at the edge”, Random Matrices Theory Appl., 5:4 (2016), 1650016, 36 pp.  crossref  mathscinet  zmath  isi
    5. J. Breuer, M. Duits, “Central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients”, J. Amer. Math. Soc., 30:1 (2017), 27–66  crossref  mathscinet  zmath  isi  scopus
    6. E. Paquette, O. Zeitouni, “Extremal eigenvalue correlations in the GUE minor process and a law of fractional logarithm”, Ann. Probab., 45:6A (2017), 4112–4166  crossref  mathscinet  zmath  isi  scopus
    7. A. Borodin, V. Gorin, A. Guionnet, “Gaussian asymptotics of discrete beta-ensembles”, Publ. Math. IHES, 2017, no. 125, 1–78  crossref  mathscinet  zmath  isi  scopus
    8. V. Gorin, L. Zhang, “Interlacing adjacent levels of $\beta$-Jacobi corners processes”, Probab. Theory Relat. Field, 172:3-4 (2018), 915–981  crossref  mathscinet  zmath  isi  scopus
    9. L. Erdos, D. Schroeder, “Fluctuations of rectangular Young diagrams of interlacing Wigner eigenvalues”, Int. Math. Res. Notices, 2018, no. 10, 3255–3298  crossref  mathscinet  zmath  isi  scopus
    10. I. Dumitriu, E. Paquette, “Spectra of overlapping Wishart matrices and the Gaussian free field”, Random Matrices-Theor. Appl., 7:2 (2018), 1850003  crossref  mathscinet  zmath  isi  scopus
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