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Teor. Veroyatnost. i Primenen., 2007, Volume 52, Issue 1, Pages 180–185 (Mi tvp13)  

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

Short Communications

Rate of convergence to the semicircle law for the Gaussian orthogonal ensemble

D. A. Timusheva, A. N. Tikhomirovb, A. A. Kholopova

a Syktyvkar State University
b St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: It is shown that the Kolmogorov distance between the expected spectral distribution function of an $n\times n$ matrix from the Gaussian orthogonal ensemble and the distribution function of the semicircle law is of order $O(n^{-1})$.

Keywords: random matrix, semicircle law, Hermite function, Gaussian ensemble.

DOI: https://doi.org/10.4213/tvp13

Full text: PDF file (544 kB)
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English version:
Theory of Probability and its Applications, 2008, 52:1, 171–177

Bibliographic databases:

Received: 26.04.2006

Citation: D. A. Timushev, A. N. Tikhomirov, A. A. Kholopov, “Rate of convergence to the semicircle law for the Gaussian orthogonal ensemble”, Teor. Veroyatnost. i Primenen., 52:1 (2007), 180–185; Theory Probab. Appl., 52:1 (2008), 171–177

Citation in format AMSBIB
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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. Bao Zh., Pan G., Zhou W., “Central Limit Theorem for Partial Linear Eigenvalue Statistics of Wigner Matrices”, J. Stat. Phys., 150:1 (2013), 88–129  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Goetze F., Tikhomirov A., “Optimal bounds for convergence of expected spectral distributions to the semi-circular law”, Probab. Theory Relat. Field, 165:1-2 (2016), 163–233  crossref  mathscinet  zmath  isi  scopus
    3. Goetze F. Naumov A. Tikhomirov A. Timushev D., “On the Local Semicircular Law For Wigner Ensembles”, Bernoulli, 24:3 (2018), 2358–2400  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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