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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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http://mi.mathnet.ru/eng/tvp153https://doi.org/10.4213/tvp153 http://mi.mathnet.ru/eng/tvp/v51/i1/p171
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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
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Fulman J., “Stein's method and characters of compact Lie groups”, Comm. Math. Phys., 288:3 (2009), 1181–1201
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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
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Haagerup U., Thorbjornsen S., “Asymptotic Expansions for the Gaussian Unitary Ensemble”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 15:1 (2012), 1250003
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Friesen O., Loewe M., “A Phase Transition for the Limiting Spectral Density of Random Matrices”, Electron. J. Probab., 18 (2013), 17, 1–17
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Roellin A., “Stein's Method in High Dimensions with Applications”, Ann. Inst. Henri Poincare-Probab. Stat., 49:2 (2013), 529–549
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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
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Hochstaettler W., Kirsch W., Warzel S., “Semicircle Law for a Matrix Ensemble with Dependent Entries”, J. Theor. Probab., 29:3 (2016), 1047–1068
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Kirsch W. Kriecherbauer T., “Semicircle Law For Generalized Curie-Weiss Matrix Ensembles At Subcritical Temperature”, J. Theor. Probab., 31:4 (2018), 2446–2458
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