On finite rank deformations of Wigner matrices

 Access to full text

1. [1] G. W. Anderson, A. Guionnet and O. Zeitouni. An Introduction to Random Matrices. Cambridge Studies in Advanced Mathematics 118. Cambridge Univ. Press, New York, 2010. Zbl1184.15023MR2760897
2. [2] Z. D. Bai. Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica9 (1999) 611–677. Zbl0949.60077MR1711663
3. [3] Z. D. Bai and J. Yao. Central limit theorems for eigenvalues in a spiked population model. Ann. Inst. Henri Poincaré Probab. Stat.44 (2008) 447–474. Zbl1274.62129MR2451053
4. [4] Z. D. Bai and Y. Q. Yin. Necessary and sufficient conditions for the almost sure convergence of the largest eigenvalue of Wigner matrices. Ann. Probab.16 (1988) 1729–1741. Zbl0677.60038MR958213
5. [5] J. Baik and J. W. Silverstein. Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal.97 (2006) 1382–1408. Zbl1220.15011MR2279680
6. [6] J. Baik, G. Ben Arous and S. Péché. Phase transition of the largest eigenvalue for non-null complex sample covariance matrices. Ann. Probab.33 (2005) 1643–1697. Zbl1086.15022MR2165575
7. [7] G. Ben Arous and A. Guionnet. Wigner matrices. In Oxford Handbook on Random Matrix Theory. G. Akemann, J. Baik and P. Di Francesco (Eds). Oxford Univ. Press, New York, 2011. Zbl1236.15063MR2932641
8. [8] F. Benaych-Georges and R. Rao. The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Unpublished manuscript. Available at arXiv:0910.2120v3. Zbl1226.15023
9. [9] F. Benaych-Georges, A. Guionnet and M. Maida. Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices. Unpublished manuscript. Available at arXiv:1009.0145. Zbl1245.60007MR2835249
10. [10] F. Benaych-Georges, A. Guionnet and M. Maida. Large deviations of the extreme eigenvalues of random deformations of matrices. Unpublished manuscript. Available at arXiv:1009.0135v2. Zbl1261.15042MR3000560
11. [11] M. Capitaine, C. Donati-Martin and D. Féral. The largest eigenvalue of finite rank deformation of large Wigner matrices: Convergence and non universality of the fluctuations. Ann. Probab.37 (2009) 1–47. Zbl1163.15026MR2489158
12. [12] M. Capitaine, C. Donati-Martin and D. Féral. Central limit theorems for eigenvalues of deformations of Wigner matrices. Ann. Inst. Henri Poincaré Probab. Stat.48 (2012) 107–133. Zbl1237.60007MR2919200
13. [13] M. Capitaine, C. Donati-MartinD. Féral and M. Février. Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices. Unpublished manuscript. Available at arXiv:1006.3684. Zbl1245.15037
14. [14] X. Chen, H. Qi and P. Tseng. Analysis of nonsmooth symmetric-matrix-valued functions with applications to semidefinite complementary problems. SIAM J. Optim.13 (2003) 960–985. Zbl1076.90042MR2005912
15. [15] E. B. Davies. The functional calculus. J. Lond. Math. Soc.52 (1995) 166–176. Zbl0858.47012MR1345723
16. [16] R. Durrett. Probability. Theory and Examples, 4th edition. Cambridge Univ. Press, New York, 2010. Zbl1202.60001MR2722836
17. [17] L. Erdös, H.-T. Yau and J. Yin. Rigidity of eigenvalues of generalized Wigner matrices. Unpublished manuscript. Available at arXiv:1007.4652. Zbl1238.15017MR2871147
18. [18] D. Féral and S. Péché. The largest eigenvalue of rank one deformation of large Wigner matrices. Comm. Math. Phys.272 (2007) 185–228. Zbl1136.82016MR2291807
19. [19] Z. Füredi and J. Komlós. The eigenvalues of random symmetric matrices. Combinatorica1 (1981) 233–241. Zbl0494.15010
20. [20] A. Guionnet and B. Zegarlinski. Lectures on logarithmic Sobolev inequalities. In Seminaire de Probabilités XXXVI. Lecture Notes in Math. 1801. Springer, Paris, 2003. Zbl1125.60111MR1971582
21. [21] B. Helffer and J. Sjöstrand. Equation de Schrödinger avec champ magnetique et equation de Harper. In Schrödinger Operators 118–197. H. Holden and A. Jensen (Eds). Lecture Notes in Physics 345. Springer, Berlin, 1989. Zbl0699.35189MR1037319
22. [22] K. Johansson. Universality for certain Hermitian Wigner matrices under weak moment conditions. Unpublished manuscript. Available at arXiv:0910.4467. Zbl1279.60014MR2919198
23. [23] A. Khorunzhy, B. Khoruzhenko and L. Pastur. Asymptotic properties of large random matrices with independent entries. J. Math. Phys.37 (1996) 5033–5060. Zbl0866.15014MR1411619
24. [24] M. Maida. Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles. Electron. J. Probab.12 (2007) 1131–1150. Zbl1127.60022MR2336602
25. [25] S. O’Rourke, D. Renfrew and A. Soshnikov. On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries. Unpublished manuscript. Available at arXiv:1104.1663v3. Zbl1280.15021MR3090549
26. [26] D. Paul. Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica17 (2007) 1617–1642. Zbl1134.62029MR2399865
27. [27] S. Péché. The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Related Fields134 (2006) 127–173. Zbl1088.15025MR2221787
28. [28] A. Pizzo, D. Renfrew and A. Soshnikov. Fluctuations of matrix entries of regular functions of Wigner matrices. Unpublished manuscript. Available at arXiv:1103.1170v3. Zbl1246.60014MR2880032
29. [29] M. Reed and B. Simon. Methods of Modern Mathematical Physics. IV: Analysis of Operators. Academic Press, New York, 1978. Zbl0242.46001MR493421
30. [30] M. Shcherbina. Central limit theorem for linear eigenvalue statistics of the Wigner and sample covariance random matrices. Zh. Mat. Fiz. Anal. Geom. 7 (2011) 176–192, 197, 199. Zbl1228.15016MR2829615
31. [31] M. Shcherbina. Letter from March 1, 2011. 
32. [32] T. Tao. Outliers in the spectrum of iid matrices with bounded rank perturbations. Unpublished manuscript. Available at arXiv:1012.4818v2. Zbl1261.60009MR3010398