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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 1, Pages 171–192 (Mi tvp153)  

This article is cited in 9 scientific papers (total in 9 papers)

Limit theorems for spectra of random matrices with martingale structure

F. Götzea, A. N. Tikhomirovb

a Bielefeld University
b Syktyvkar State University

Abstract: We study classical ensembles of real symmetric random matrices introduced by Eugene Wigner. We discuss Stein's method for the asymptotic approximation of expectations of functions of the normalized eigenvalue counting measure of high dimensional matrices. The method is based on a differential equation for the density of the semicircle law.

Keywords: random matrices, Stein's method, semicircle law.

DOI: https://doi.org/10.4213/tvp153

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English version:
Theory of Probability and its Applications, 2007, 51:1, 42–64

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Received: 20.12.2003
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Citation: F. Götze, A. N. Tikhomirov, “Limit theorems for spectra of random matrices with martingale structure”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 171–192; Theory Probab. Appl., 51:1 (2007), 42–64

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. Bogatyrev S.A., Götze F., Ulyanov V.V., “Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space”, J. Multivariate Anal., 97:9 (2006), 2041–2056  crossref  mathscinet  zmath  isi  elib  scopus
    2. Fulman J., “Stein's method and characters of compact Lie groups”, Comm. Math. Phys., 288:3 (2009), 1181–1201  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Chatterjee S., Fulman J., Röllin A., “Exponential approximation by Stein's method and spectral graph theory”, ALEA Lat. Am. J. Probab. Math. Stat., 8 (2011), 197–223  mathscinet  zmath  isi
    4. Haagerup U., Thorbjornsen S., “Asymptotic Expansions for the Gaussian Unitary Ensemble”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 15:1 (2012), 1250003  crossref  mathscinet  zmath  isi  elib  scopus
    5. Friesen O., Loewe M., “A Phase Transition for the Limiting Spectral Density of Random Matrices”, Electron. J. Probab., 18 (2013), 17, 1–17  crossref  mathscinet  isi  scopus
    6. Roellin A., “Stein's Method in High Dimensions with Applications”, Ann. Inst. Henri Poincare-Probab. Stat., 49:2 (2013), 529–549  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. F. Götze, A. A. Naumov, A. N. Tikhomirov, “Limit theorems for two classes of random matrices with dependent entries”, Theory Probab. Appl., 59:1 (2015), 23–39  mathnet  crossref  crossref  mathscinet  isi  elib
    8. Hochstaettler W., Kirsch W., Warzel S., “Semicircle Law for a Matrix Ensemble with Dependent Entries”, J. Theor. Probab., 29:3 (2016), 1047–1068  crossref  mathscinet  zmath  isi  scopus
    9. Kirsch W. Kriecherbauer T., “Semicircle Law For Generalized Curie-Weiss Matrix Ensembles At Subcritical Temperature”, J. Theor. Probab., 31:4 (2018), 2446–2458  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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