Spectra of Random Gaussian g-Cyclic Matrices

Previous article Next article Spectra of Random Gaussian g-Cyclic MatricesB. V. RyazanovB. V. Ryazanovhttps://doi.org/10.1137/1123063PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. M. Vinogradov, Foundations of the Theory of Numbers, Nauka, Moscow, 1965, (In Russian.) Google Scholar[2] V. L. Girko, Random Matrices, Visha Shkola, Kiev, 1975, (In Russian.) 0344.60001 Google Scholar[3A] Freeman J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Mathematical Phys., 3 (1962), 140–156 10.1063/1.1703773 MR0143556 0105.41604 CrossrefGoogle Scholar[3B] Freeman J. Dyson, Statistical theory of the energy levels of complex systems. II, J. Mathematical Phys., 3 (1962), 157–165 10.1063/1.1703774 MR0143557 0105.41604 CrossrefGoogle Scholar[3C] Freeman J. Dyson, Statistical theory of the energy levels of complex systems. III, J. Mathematical Phys., 3 (1962), 166–175 10.1063/1.1703775 MR0143558 0105.41604 CrossrefGoogle Scholar[3D] Freeman J. Dyson and , Madan Lal Mehta, Statistical theory of the energy levels of complex systems. IV, J. Mathematical Phys., 4 (1963), 701–712 10.1063/1.1704008 MR0151231 0133.45201 CrossrefGoogle Scholar[4] V. M. Dubner, The distribution of the eigenvalues of random cyclic matrices, Theory Prob. Applications, 14 (1969), 342–344 10.1137/1114044 LinkGoogle Scholar[5] Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965xvii+508 MR0197234 0193.34701 Google Scholar[6] M. Markus and , H. Mink, A Review of the Theory of Matrices and Matrix Inequalities, Nauka, Moscow, 1972, (In Russian.) Google Scholar[7] L. A. Pastur, Spectra of random selfadjoint operators, Uspehi Mat. Nauk, 28 (1973), 3–64, (In Russian.) MR0406251 Google Scholar[8] C. M. Ablow and , J. L. Brenner, Roots and canonical forms for circulant matrices, Trans. Amer. Math. Soc., 107 (1963), 360–376 MR0155841 0112.25003 CrossrefGoogle Scholar[9] M. L. Mehta, Random matrices and the statistical theory of energy levels, Academic Press, New York, 1967x+259 MR0220494 0925.60011 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Circular LawV. L. Girko17 July 2006 | Theory of Probability & Its Applications, Vol. 29, No. 4AbstractPDF (841 KB) Volume 23, Issue 3| 1979Theory of Probability & Its Applications History Submitted:31 May 1976Published online:17 July 2006 InformationCopyright © 1979 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1123063Article page range:pp. 543-558ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics