The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


1. G. Anderson, A. Guionnet, and O. Zeitouni. An Introduction to Random Matrices . Cambridge University Press, 2009. MR2760897.
2. A. I. Aptekarev, P. M. Bleher, and A. B. J. Kuijlaars. Large n limit of Gaussian random matrices with external source. II. Comm. Math. Phys., 259(2):367--389, 2005. MR2172687.
3. Z. D. Bai. Methodologies in spectral analysis of large-dimensional random matrices, a review. Statist. Sinica , 9(3):611--677, 1999. With comments by G. J. Rodgers and Jack W. Silverstein; and a rejoinder by the author. MR1711663.
4. Z. D. Bai and J. W. Silverstein. No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Probab., 26(1):316--345, 1998. MR1617051.
5. Z. D. Bai and J. W. Silverstein. Exact separation of eigenvalues of large-dimensional sample covariance matrices. Ann. Probab., 27(3):1536--1555, 1999. MR1733159.
6. Z. D. Bai and J. Yao. Limit theorems for sample eigenvalues in a generalized spiked population model. ArXiv e-prints , June 2008.
7. Z. D. Bai and Y. Q. Yin. Necessary and sufficient conditions for almost sure convergence of the largest eigenvalue of a Wigner matrix. Ann. Probab. , 16(4):1729--1741, 1988. MR0958213.
8. J. Baik, G. Ben Arous, and S. Péché. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab., 33(5):1643--1697, 2005. MR2165575.
9. J. Baik and J. W. Silverstein. Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal., 97(6):1382--1408, 2006. MR2279680.
10. S. T. Belinschi and H. Bercovici. A new approach to subordination results in free probability. J. Anal. Math., 101:357--365, 2007. MR2346550.
11. F. Benaych-Georges and R. R. Nadakuditi. The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Advances in Mathematics, 227(1): 494--521, 2011. MR2782201.
12. P. Biane. On the free convolution with a semi-circular distribution. Indiana Univ. Math. J., 46(3):705--718, 1997. MR1488333.
13. P. Biane. Processes with free increments. Math. Z., 227(1):143--174, 1998. MR1605393.
14. P. Bleher and A. B. J. Kuijlaars. Large n limit of Gaussian random matrices with external source. I. Comm. Math. Phys., 252(1-3):43--76, 2004. MR2103904.
15. P. M. Bleher and A. B. J. Kuijlaars. Large n limit of Gaussian random matrices with external source. III. Double scaling limit. Comm. Math. Phys., 270(2):481--517, 2007. MR2276453.
16. S. G. Bobkov and F. Gotze. Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal., 163(1):1--28, 1999. MR1682772.
17. M. Capitaine and C. Donati-Martin. Strong asymptotic freeness for Wigner and Wishart matrices. Indiana Univ. Math. J., 56(2):767--803, 2007. MR2317545.
18. M. Capitaine, C. Donati-Martin, and D. Féral. The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations. Ann. Probab., 37(1):1--47, 2009. MR2489158.
19. K. Dykema. On certain free product factors via an extended matrix model. J. Funct. Anal., 112(1):31--60, 1993. MR1207936.
20. D. Féral and S. Péché. The largest eigenvalue of rank one deformation of large Wigner matrices. Comm. Math. Phys., 272(1):185--228, 2007. MR2291807.
21. W. Fulton. Eigenvalues of sums of Hermitian matrices (after A. Klyachko). Astérisque, (252):Exp. No. 845, 5, 255--269, 1998. Séminaire Bourbaki. Vol. 1997/98. MR1685640.
22. Z. Furedi and J. Komlos. The eigenvalues of random symmetric matrices. Combinatorica, 1(3):233--241, 1981. MR0637828.
23. U. Haagerup and S. Thorbjornsen. A new application of random matrices: Ext ( C* red(F_2)) is not a group. Ann. of Math. (2), 162(2):711--775, 2005. MR2183281.
24. R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge University Press, Cambridge, 1990. Corrected reprint of the 1985 original. MR1084815.
25. A. M. Khorunzhy, B. A. Khoruzhenko and L. A. Pastur. Asymptotic properties of large random matrices with independent entries. J. Math. Phys., 37(10):5033--5060, 1996. MR1411619.
26. C. Male. The norm of polynomials in large random and deterministic matrices. Probab. Theory and Related Fields, Online First DOI: 10.1007/s00440-011-0375-2, 2011.
27. J. Mingo and R. Speicher. Free probability and Random matrices. Personal Communication, 2010.
28. R. R. Nadakuditi and J. W. Silverstein. Fundamental limit of sample generalized eigenvalue based detection of signals in noise using relatively few signal-bearing and noise-only samples. IEEE Journal of Selected Topics in Signal Processing, 4(3):468--480, 2010.
29. L. Pastur and A. Lejay. Matrices aléatoires: statistique asymptotique des valeurs propres. In S éminaire de Probabilit és, XXXVI , volume 1801 of Lecture Notes in Math.: 135--164. Springer, Berlin, 2003. MR1971583.
30. S. Péché. The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Related Fields, 134:127 - -173, 2006. MR2221787.
31. H. Schultz. Non-commutative polynomials of independent Gaussian random matrices. The real and symplectic cases. Probab. Theory Related Fields, 131(2):261--309, 2005. MR2117954.
32. H. G. Tillmann. Randverteilungen analytischer Funktionen und Distributionen. Math. Z., 59:61--83, 1953. MR0057345.
33. D. Voiculescu. Limit laws for random matrices and free products. Invent. Math., 104(1):201--220, 1991. MR1094052.
34. D. Voiculescu. The analogues of entropy and of Fisher's information measure in free probability theory. I. Comm. Math. Phys., 155(1):71--92, 1993. MR1228526.
35. D. V. Voiculescu, K. J. Dykema, and A. Nica. Free random variables, A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. volume 1 of CRM Monograph Series. American Mathematical Society, Providence, RI, 1992. MR1217253.
36. E. P. Wigner. Characteristic vectors of bordered matrices with infinite dimensions. Ann. of Math. (2), 62:548--564, 1955. MR0077805.
37. E. P. Wigner. On the distribution of the roots of certain symmetric matrices. Ann. of Math. (2), 67:325--327, 1958. MR0095527.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.