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References

  1. Z. D. Bai. Circular law, Ann. Probab. 25 (1997), no. 1, 494-529. Math. Review 98k:60040
  2. Z. D. Bai, J. W. Silverstein. Spectral Analysis of Large Dimensional Random Matrices, Mathematics Monograph Series 2, Science Press, Beijing (2006). Math. Review 2567175
  3. Ch. Bordenave, P. Caputo, D. Chafai. Circular Law Theorem for Random Markov Matrices, preprint arXiv:0808.1502v2.
  4. D. Chafai. Circular law for noncentral random matrices. J. Theoret. Probab. 23 (2010), 945-950. Math. Review number not available.
  5. B. Dozier and J. Silverstein. On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices, J. Multivar. Anal. 98 (2007), no. 4, 678-694. Math. Review 2009d:60078
  6. A. Edelman, The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law, J. Multivar. Anal. 60 (1997), no. 2, 203-232. Math. Review 98b:15025
  7. P. Forrester and A. Mays, Pfa?an point process for the gaussian real generalised eigen- value problem, preprint arXiv:0910.2531.
  8. V. L. Girko, The circular law, Teor. Veroyatnost. i Primenen. 29 (1984), no. 4, 669-679. Math. Review 87c:15042
  9. V. L. Girko, Strong circular law, Random Oper. Stochastic Equations 5 (1997), no. 2, 173-196. Math. Review 98m:15044
  10. V. L. Girko, The circular law. Twenty years later. III, Random Oper. Stochastic Equations 13 (2005), no. 1, 53-109. Math. Review 2007e:60023
  11. I. Y. Goldsheid and B. A. Khoruzhenko, The Thouless formula for random non-Hermitian Jacobi matrices, Israel J. Math. 148 (2005), 331-346, Probability in mathematics. Math. Review 2191234
  12. F. Gotze and A. Tikhomirov, The Circular Law for Random Matrices, preprint to appear in Ann. of Probab. arXiv:math/07093995.
  13. F. Gotze and A. Tikhomirov, On the asymptotic spectrum of products of independent random matrices, preprint arXiv:math/1012.2710.
  14. A. Guionnet, M. Krishnapur, and O. Zeitouni, The single ring theorem, preprint arXiv:0909.2214.
  15. R. Horn and C. Johnson, Topics in matrix analysis, Cambridge University Press, Cambridge, (1991). Math. Review 92e:15003
  16. C.-R. Hwang, A brief survey on the spectral radius and the spectral distribution of large random matrices with i.i.d. entries, Random matrices and their applications (Brunswick, Maine, 1984), Contemp. Math., vol. 50, Amer. Math. Soc., Providence, RI (1986), pp. 145- 152. Math. Review 87m:60080
  17. M. Krishnapur, From random matrices to random analytic functions, Ann. Probab. 37 (2009), no. 1, 314-346. Math. Review 2010d:30055
  18. V.A. Marchenko and L.A. Pastur, The distribution of eigenvalues in sertain sets of random matrices, Mat. Sb. 72 (1967), 507-536. Math. Review 0208649
  19. M. L. Mehta, Random matrices and the statistical theory of energy levels, Academic Press, New York, (1967). Math. Review 0220494
  20. G.M. Pan and W. Zhou, Circular law, extreme singular values and potential theory, J. Multivar. Anal. 101 (2010), no. 3, 645-656. Math. Review 2011a:60033
  21. T. Rogers, Universal sum and product rules for random matrices, J. Math. Phys. 51 (2010), no. 093304. Math. Review number not available.
  22. P. Sniady, Random regularization of Brown spectral measure, J. Funct. Anal. 193 (2002), no. 2, 291-313. Math. Review 2003k:15029
  23. T. Tao and V. Vu, Random matrices: the circular law, Commun. Contemp. Math. 10 (2008), no. 2, 261-307. Math. Review 2009d:60091
  24. T. Tao and V. Vu, Random matrices: Universality of ESDs and the circular law, preprint to appear in Ann. Probab. arXiv:0807.4898 [math.PR].
  25. K. W. Wachter, The strong limits of random matrix spectra for sample matrices of inde- pendent elements, Ann. Probab. 6 (1978), no. 1, 1-18. Math. Review 0467894
  26. Y. Q. Yin, Limiting spectral distribution for a class of random matrices, J. Multivar. Anal. 20 (1986), no. 1, 50-68. Math. Review 0862241


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