Erratum to Outliers in the spectrum of iid matrices with bounded rank perturbations (Probab. Theory Relat. Fields, (2013), 155, (231-263), 10.1007/s00440-011-0397-9);Outliers in the spectrum of iid matrices with bounded rank perturbations

Probability Theory and Related Fields

Volumn 155, Issue 1-2, 2013, Pages 231-263

  Tao, Terence ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84872653524     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-013-0513-0     Document Type: Erratum

References (44)

1. Alon N., Krivelevich M., Vu V. H.: On the concentration of eigenvalues of random symmetric matrices. Isr. J. Math. 131, 259-267 (2002).
2. Andrew A.: Eigenvalues and singular values of certain random matrices. J. Comput. Appl. Math. 30(2), 165-171 (1990).
3. Arbenz P., Gander W., Golub G.: Restricted rank modification of the symmetric eigenvalue problem: Theoretical considerations. Linear Algebra Appl. 104, 75-95 (1988).
4. Bai Z. D.: Circular law. Ann. Probab. 25, 494-529 (1997).
5. Bai Z. D., Silverstein J.: Exact separation of eigenvalues of large-dimensional sample covariance matrices. Ann. Probab. 27(3), 1536-1555 (1999).
6. Bai Z. D., Silverstein J.: Spectral analysis of large dimensional random matrices. Mathematics Monograph Series. vol. 2, Science Press, Beijing (2006).
7. Baik J., Silverstein J.: Eigenvalues of large sample covariance matrices of spiked population models (English summary). J. Multivariate Anal. 97(6), 1382-1408 (2006).
8. Bai D., Yao J.-F.: Central limit theorems for eigenvalues in a spiked population model. Ann. I. H. P. Prob. et Stat. 44(3), 447-474 (2008).
9. Bai Z. D., Yin Y. Q.: Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix. Ann. Probab. 16(4), 1729-1741 (1988).
10. Bai Z. D., Yin Y. Q.: Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang. Probab. Theory Relat. Fields 73, 555-569 (1986).
11. Baik J., Ben Arous G., Peche S.: Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33(5), 1643-1697 (2005).
12. Baik J., Silverstein J.: Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97(6), 1382-1408 (2006).
13. Benaych-Georges, F., Rao, R.: The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices (preprint).
14. Benaych-Georges, F., Guionnet, A., Maida, M.: Large deviations of the extreme eigenvalues of random deformations of matrices (preprint).
15. Benaych-Georges, F., Guionnet, A., Maida, M.: Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices (preprint).
16. Bordenave, C.: On the spectrum of sum and product of non-hermitian random matrices. Available at http://arxiv. org/abs/1010. 3087 (preprint).
17. Bordenave, C., Caputo, P., Chafaï, D.: Circular law theorem for random Markov matrices. Available at http://arxiv. org/abs/0808. 1502 (preprint).
18. Capitaine, M., Donati-Martin, C., Féral, D.: Central limit theorems for eigenvalues of deformations of Wigner matrices. preprint. Available at http://arxiv. org/abs/0903. 4740.
19. Chafai D.: Circular law for non-central random matrices. J. Theor. Probab. 23, 945-950 (2010).
20. Feller W.: An introduction to probability theory and its applications. vol. II, Wiley, New York (1971).
21. Féral D., Péché S.: The largest eigenvalue of rank one deformation of large Wigner matrices. Commun. Math. Phys. 272, 185-228 (2007).
22. Geman S.: The spectral radius of large random matrices. Ann. Probab. 14, 1318-1328 (1986).
23. Ginibre J.: Statistical ensembles of complex, quaternion, and real matrices. J. Math. Phys. 6, 440-449 (1965).
24. Girko, V. L.: Circular law. Theory Probab. Appl. 694-706 (1984).
25. Girko V. L.: The strong circular law. Twenty years later. II. Random Oper. Stoch. Equ. 12(3), 255-312 (2004).
26. Götze, F., Tikhomirov, A. N.: On the circular law. Available at http://arxiv. org/abs/math/0702386.
27. Götze F., Tikhomirov A. N.: The circular law for random matrices. Ann. Probab. 38(4), 1444-1491 (2010).
28. Guionnet A., Zeitouni O.: Concentration of the spectral measure for large matrices. Electron. Commun. Probab. 5, 119-136 (2000).
29. Hough B. J., Krishnapur M., Peres Y., Virág B.: Zeros of Gaussian analytic functions and determinantal point processes. University Lecture Series, 51. American Mathematical Society, Providence (2009).
30. Ledoux M.: The Concentration of Measure Phenomenon. American Mathematical Society, Providence (2001).
31. Litvak A., Pajor A., Rudelson M., Tomczak-Jaegermann N.: Smallest singular value of random matrices and geometry of random polytopes. Adv. Math. 195(2), 491-523 (2005).
32. Meckes M.: Concentration of norms and eigenvalues of random matrices. J. Funct. Anal. 211(2), 508-524 (2004).
33. Mehta M. L.: Random Matrices and the Statistical Theory of Energy Levels. Academic Press, New York (1967).
34. Pan G., Zhou W.: Circular law, extreme singular values and potential theory. J. Multivariate Anal. 101(3), 645-656 (2010).
35. Peche S.: The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Relat. Fields 134(1), 127-173 (2006).
36. Peres Y., Virág B.: Zeros of the i. i. d. Gaussian power series: a conformally invariant determinantal process. Acta Math. 194(1), 1-35 (2005).
37. Pizzo, A., Renfrew, D., Soshnikov, A.: On finite rank deformations of Wigner matrices (preprint).
38. Prosen T.: Exact statistics of complex zeros for Gaussian random polynomials with real coefficients. J. Phys. A Math. Gen. 29, 4417-4423 (1996).
39. Rajan K., Abbott L. F.: Eigenvalue spectra of random matrices for neural networks. Phys. Rev. Lett. 97, 188104 (2006).
40. Rudelson M., Vershynin R.: The Littlewood-Offord problem and invertibility of random matrices. Adv. Math. 218(2), 600-633 (2008).
41. Silverstein J.: The spectral radii and norms of large-dimensional non-central random matrices. Commun. Stat. Stoch. Models 10(3), 525-532 (1994).
42. Tao T., Vu V.: Random matrices: the circular law. Commun. Contemp. Math. 10, 261-307 (2008).
43. Tao, T., Vu, V.: Smooth analysis of the condition number and the least singular value. Available at http://arxiv. org/abs/0805. 3167 (preprint).
44. Tao T., Vu V., Krishnapur M.: Random matrices: universality of ESDs and the circular law. Ann. Probab. 38(5), 2023-2065 (2010).