Elliptic Law

Abstract

Previous article Next article Elliptic LawV. L. GirkoV. L. Girkohttps://doi.org/10.1137/1130089PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Eugene P. Wigner, On the distribution of the roots of certain symmetric matrices, Ann. of Math. (2), 67 (1958), 325–327 20:2029 0085.13203 CrossrefGoogle Scholar[2] L. Arnold, On the asymptotic distribution of the eigenvalues of random matrices, J. Math. Anal. Appl., 20 (1960), 262–268 10.1016/0022-247X(67)90089-3 0246.60029 CrossrefGoogle Scholar[3] Ulf Grenander, Probabilities on algebraic structures, John Wiley & Sons Inc., New York, 1963, 218– 34:6810 0131.34804 Google Scholar[4] M. L. Mehta, Random matrices and the statistical theory of energy levels, Academic Press, New York, 1967x+259 36:3554 0925.60011 Google Scholar[5] L. A. Pastur, The spectrum of random matrices, Teoret. Mat. Fiz., 10 (1972), 102–112, (In Russian.) 57:15106 Google Scholar[6] F. A. Berezin, Some remarks on the Wigner distribution, Teoret. Mat. Fiz., 17 (1973), 305–318, (In Russian.) 57:4924 Google Scholar[7] V. L. Girko, Random Matrices, Vishcha Shkola, Kiev, 1975, (In Russian.) Google Scholar[8] Jean Ginibre, Statistical ensembles of complex, quaternion, and real matrices, J. Mathematical Phys., 6 (1965), 440–449 30:3936 0127.39304 CrossrefGoogle Scholar[9] V. L. Girko, Theory of Random Determinants, Vishcha Shkola, Kiev, 1980, (In Russian.) Google Scholar[10] V. L. Girko, V-transformation, Dokl. Akad. Nauk Ukrain. SSR Ser. A, (1982), 5–6, 86 83e:60032 0509.60032 Google Scholar[11] V. L. Girko, The circular law, Theory Prob. Appl., 29 (1984), 694–706 LinkGoogle Scholar[12] V. L. Girko, General limit theorems for spectral functions of random matrices, Theory Prob. Appl., 22 (1977), 156–160 0374.60038 LinkGoogle Scholar[13] V. V. Petrov, Sums of independent random variables, Springer-Verlag, New York, 1975x+346 52:9335 CrossrefGoogle Scholar[14] N. I. 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Noordhoff Ltd., Groningen, 1963xxxi+718 31:920 0124.17404 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Equilibrium in a large Lotka–Volterra system with pairwise correlated interactionsStochastic Processes and their Applications, Vol. 153 Cross Ref The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element7 March 2022 | Letters in Mathematical Physics, Vol. 112, No. 2 Cross Ref Eigenvalues of Random Matrices with Generalized Correlations: A Path Integral Approach22 March 2022 | Physical Review Letters, Vol. 128, No. 12 Cross Ref Spectrum of heavy-tailed elliptic random matricesElectronic Journal of Probability, Vol. 27, No. none Cross Ref Real Eigenvalues of Elliptic Random Matrices9 November 2021 | International Mathematics Research Notices, Vol. 43 Cross Ref Eikonal formulation of large dynamical random matrix models15 November 2021 | Physical Review E, Vol. 104, No. 5 Cross Ref Counting 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1984Published online:28 July 2006 InformationCopyright © 1986 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1130089Article page range:pp. 677-690ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics