The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
W. Hachem; P. Loubaton; J. Najim
Annales de l'I.H.P. Probabilités et statistiques (2006)
- Volume: 42, Issue: 6, page 649-670
- ISSN: 0246-0203
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topHachem, W., Loubaton, P., and 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 42.6 (2006): 649-670. <http://eudml.org/doc/77913>.
@article{Hachem2006,
author = {Hachem, W., Loubaton, P., Najim, J.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {random matrix; Stieltjes transform; convergence},
language = {eng},
number = {6},
pages = {649-670},
publisher = {Elsevier},
title = {The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile},
url = {http://eudml.org/doc/77913},
volume = {42},
year = {2006},
}
TY - JOUR
AU - Hachem, W.
AU - Loubaton, P.
AU - Najim, J.
TI - The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 6
SP - 649
EP - 670
LA - eng
KW - random matrix; Stieltjes transform; convergence
UR - http://eudml.org/doc/77913
ER -
References
top- [1] Z.D. Bai, Methodologies in spectral analysis of large-dimensional random matrices, a review, Statist. Sinica9 (3) (1999) 611-677. Zbl0949.60077MR1711663
- [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. Zbl0937.60017MR1617051
- [3] A. Boutet de Monvel, A. Khorunzhy, V. Vasilchuk, Limiting eigenvalue distribution of random matrices with correlated entries, Markov Process. Related Fields2 (4) (1996) 607-636. Zbl0884.15018MR1431189
- [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. Theory48 (3) (2002) 637-650. Zbl1071.94500MR1889973
- [5] M. Debbah, W. Hachem, P. Loubaton, M. de Courville, MMSE analysis of certain large isometric random precoded systems, IEEE Trans. Inform. Theory49 (5) (2003) 1293-1311. Zbl1063.94055MR1984828
- [6] R.B. Dozier, J.W. Silverstein, On the empirical distribution of eigenvalues of large dimensional information-plus-noise type matrices. Preprint, 2004. Zbl1115.60035MR2322123
- [7] V.L. Girko, Theory of Random Determinants, Math. Appl. (Soviet Ser.), vol. 45, Kluwer Academic Publishers Group, Dordrecht, 1990. Zbl0704.60003MR1080966
- [8] V.L. Girko, Theory of stochastic canonical equations. Vol. I, Math. Appl., vol. 535, Kluwer Academic Publishers, Dordrecht, 2001. Zbl0996.60002MR1887675
- [9] A. Goldsmith, S.A. Jafar, N. Jindal, S. Vishwanath, Capacity limits of mimo channels, IEEE J. Sel. Areas in Comm.21 (5) (2003). Zbl1043.94006
- [10] W. Hachem, P. Loubaton, J. Najim, Deterministic equivalents for certain functionals of large random matrices, Available at http://arxiv.org/, math.PR/0507172. Zbl1181.15043MR2326235
- [11] W. Hachem, P. Loubaton, J. Najim, The empirical eigenvalue distribution of a Gram Matrix: From independence to stationarity, Markov Process. Related Fields11 (4) (2005) 629-648. Zbl1101.15016MR2191967
- [12] T. Kailath, A.H. Sayed, B. Hassibi, Linear Estimation, Prentice-Hall, Englewood Cliffs, NJ, 2000. Zbl0980.93077
- [13] A. Khorunzhy, B. Khoruzhenko, L. Pastur, Asymptotic properties of large random matrices with independent entries, J. Math. Phys.37 (10) (1996) 5033-5060. Zbl0866.15014MR1411619
- [14] L. Li, A.M. Tulino, S. Verdu, Design of reduced-rank mmse multiuser detectors using random matrix methods, IEEE Trans. Inform. Theory50 (6) (2004) 986-1008. Zbl1303.94017MR2094863
- [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. Zbl0152.16101MR208649
- [16] D. Shlyakhtenko, Random Gaussian band matrices and freeness with amalgamation, Int. Math. Res. Notices20 (1996) 1013-1025. Zbl0872.15018MR1422374
- [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. Zbl0851.62015MR1370408
- [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. Zbl0833.60038MR1345534
- [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. Theory45 (2) (1999) 641-657. Zbl0946.94003MR1677023
- [21] D. Tse, O. Zeitouni, Linear multiuser receivers in random environments, IEEE Trans. Inform. Theory46 (1) (2000) 171-188. Zbl1051.62528
- [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. Zbl1133.94014
- [23] Y.Q. Yin, Limiting spectral distribution for a class of random matrices, J. Multivariate Anal.20 (1) (1986) 50-68. Zbl0614.62060MR862241
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