The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
Hachem, W. ; Loubaton, P. ; Najim, J.
Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006), p. 649-670 / Harvested from Numdam
@article{AIHPB_2006__42_6_649_0,
     author = {Hachem, W. and Loubaton, P. and Najim, J.},
     title = {The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {42},
     year = {2006},
     pages = {649-670},
     doi = {10.1016/j.anihpb.2005.10.001},
     mrnumber = {2269232},
     zbl = {1109.15021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2006__42_6_649_0}
}
Hachem, W.; Loubaton, P.; Najim, J. The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) pp. 649-670. doi : 10.1016/j.anihpb.2005.10.001. http://gdmltest.u-ga.fr/item/AIHPB_2006__42_6_649_0/

[1] Z.D. Bai, Methodologies in spectral analysis of large-dimensional random matrices, a review, Statist. Sinica 9 (3) (1999) 611-677. | MR 1711663 | Zbl 0949.60077

[2] Z.D. Bai, J.W. Silverstein, No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices, Ann. Probab. 26 (1) (1998) 316-345. | MR 1617051 | Zbl 0937.60017

[3] A. Boutet De Monvel, A. Khorunzhy, V. Vasilchuk, Limiting eigenvalue distribution of random matrices with correlated entries, Markov Process. Related Fields 2 (4) (1996) 607-636. | MR 1431189 | Zbl 0884.15018

[4] C.N. Chuah, J.M. Kahn, D.N.C. Tse, R.A. Valenzuela, Capacity scaling in mimo wireless systems under correlated fading, IEEE Trans. Inform. Theory 48 (3) (2002) 637-650. | MR 1889973 | Zbl 1071.94500

[5] M. Debbah, W. Hachem, P. Loubaton, M. De Courville, MMSE analysis of certain large isometric random precoded systems, IEEE Trans. Inform. Theory 49 (5) (2003) 1293-1311. | MR 1984828 | Zbl 1063.94055

[6] R.B. Dozier, J.W. Silverstein, On the empirical distribution of eigenvalues of large dimensional information-plus-noise type matrices. Preprint, 2004. | MR 2322123

[7] V.L. Girko, Theory of Random Determinants, Math. Appl. (Soviet Ser.), vol. 45, Kluwer Academic Publishers Group, Dordrecht, 1990. | MR 1080966 | Zbl 0704.60003

[8] V.L. Girko, Theory of stochastic canonical equations. Vol. I, Math. Appl., vol. 535, Kluwer Academic Publishers, Dordrecht, 2001. | MR 1887675 | Zbl 0996.60002

[9] A. Goldsmith, S.A. Jafar, N. Jindal, S. Vishwanath, Capacity limits of mimo channels, IEEE J. Sel. Areas in Comm. 21 (5) (2003).

[10] W. Hachem, P. Loubaton, J. Najim, Deterministic equivalents for certain functionals of large random matrices, Available at http://arxiv.org/, math.PR/0507172. | MR 2326235

[11] W. Hachem, P. Loubaton, J. Najim, The empirical eigenvalue distribution of a Gram Matrix: From independence to stationarity, Markov Process. Related Fields 11 (4) (2005) 629-648. | MR 2191967 | Zbl 1101.15016

[12] T. Kailath, A.H. Sayed, B. Hassibi, Linear Estimation, Prentice-Hall, Englewood Cliffs, NJ, 2000.

[13] A. Khorunzhy, B. Khoruzhenko, L. Pastur, Asymptotic properties of large random matrices with independent entries, J. Math. Phys. 37 (10) (1996) 5033-5060. | MR 1411619 | Zbl 0866.15014

[14] L. Li, A.M. Tulino, S. Verdu, Design of reduced-rank mmse multiuser detectors using random matrix methods, IEEE Trans. Inform. Theory 50 (6) (2004) 986-1008. | MR 2094863

[15] V.A. Marčenko, L.A. Pastur, Distribution of eigenvalues in certain sets of random matrices, Mat. Sb. (N.S.) 72 (114) (1967) 507-536. | MR 208649 | Zbl 0152.16101

[16] D. Shlyakhtenko, Random Gaussian band matrices and freeness with amalgamation, Int. Math. Res. Notices 20 (1996) 1013-1025. | MR 1422374 | Zbl 0872.15018

[17] J.W. Silverstein, Strong convergence of the empirical distribution of eigenvalues of large-dimensional random matrices, J. Multivariate Anal. 55 (2) (1995) 331-339. | MR 1370408 | Zbl 0851.62015

[18] J.W. Silverstein, Z.D. Bai, On the empirical distribution of eigenvalues of a class of large-dimensional random matrices, J. Multivariate Anal. 54 (2) (1995) 175-192. | MR 1345534 | Zbl 0833.60038

[19] J.W. Silverstein, P.L. Combettes, Signal detection via spectral theory of large dimensional random matrices, IEEE Trans. Signal Process. 40 (8) (1992) 2100-2105.

[20] D. Tse, S. Hanly, Linear multiuser receivers: effective interference, effective bandwidth and user capacity, IEEE Trans. Inform. Theory 45 (2) (1999) 641-657. | MR 1677023 | Zbl 0946.94003

[21] D. Tse, O. Zeitouni, Linear multiuser receivers in random environments, IEEE Trans. Inform. Theory 46 (1) (2000) 171-188. | Zbl 1051.62528

[22] A. Tulino, S. Verdu, Random Matrix Theory and Wireless Communications, Fondations and Trends in Communications and Information Theory, vol. 1, Now Publishers, Delft, 2004. | Zbl 05129495

[23] Y.Q. Yin, Limiting spectral distribution for a class of random matrices, J. Multivariate Anal. 20 (1) (1986) 50-68. | MR 862241 | Zbl 0614.62060