Consider a non-centered matrix with a separable variance profile:
Considérons une matrice , non centrée, de taille , avec un profil de variance séparable :
Keywords: random matrix, empirical distribution of the eigenvalues, Stieltjes transform
@article{AIHPB_2013__49_1_36_0, author = {Hachem, Walid and Loubaton, Philippe and Najim, Jamal and Vallet, Pascal}, title = {On bilinear forms based on the resolvent of large random matrices}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {36--63}, publisher = {Gauthier-Villars}, volume = {49}, number = {1}, year = {2013}, doi = {10.1214/11-AIHP450}, mrnumber = {3060147}, zbl = {1272.15020}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/11-AIHP450/} }
TY - JOUR AU - Hachem, Walid AU - Loubaton, Philippe AU - Najim, Jamal AU - Vallet, Pascal TI - On bilinear forms based on the resolvent of large random matrices JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 36 EP - 63 VL - 49 IS - 1 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/11-AIHP450/ DO - 10.1214/11-AIHP450 LA - en ID - AIHPB_2013__49_1_36_0 ER -
%0 Journal Article %A Hachem, Walid %A Loubaton, Philippe %A Najim, Jamal %A Vallet, Pascal %T On bilinear forms based on the resolvent of large random matrices %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 36-63 %V 49 %N 1 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/11-AIHP450/ %R 10.1214/11-AIHP450 %G en %F AIHPB_2013__49_1_36_0
Hachem, Walid; Loubaton, Philippe; Najim, Jamal; Vallet, Pascal. On bilinear forms based on the resolvent of large random matrices. Annales de l'I.H.P. Probabilités et statistiques, Volume 49 (2013) no. 1, pp. 36-63. doi : 10.1214/11-AIHP450. http://archive.numdam.org/articles/10.1214/11-AIHP450/
[1] On the precoder design of flat fading MIMO systems equipped with MMSE receivers: A large-system approach. IEEE Trans. Inform. Theory 57 (2011) 4138-4155. | MR
and .[2] On asymptotics of eigenvectors of large sample covariance matrix. Ann. Probab. 35 (2007) 1532-1572. | MR | Zbl
, and .[3] No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Probab. 26 (1998) 316-345. | MR | Zbl
and .[4] Exact separation of eigenvalues of large-dimensional sample covariance matrices. Ann. Probab. 27 (1999) 1536-1555. | MR | Zbl
and .[5] No eigenvalues outside the support of the limiting spectral distribution of information-plus-noise type matrices. Random Matrices Theory Appl. 1 (2012) 1150004. | MR | Zbl
and .[6] The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Preprint, 2009. Available at arXiv:0910.2120. | Zbl
and .[7] On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices. J. Multivariate Anal. 98 (2007) 678-694. | MR | Zbl
and .[8] The largest eigenvalues of finite rank deformation of large Wigner matrices: Convergence and nonuniversality of the fluctuations. Ann. Probab. 37 (2009) 1-47. | MR | Zbl
, and .[9] On the capacity achieving covariance matrix for Rician MIMO channels: An asymptotic approach. IEEE Trans. Inform. Theory 56 (2010) 1048-1069. | MR
, , , and .[10] Rigidity of eigenvalues of generalized Wigner matrices. Unpublished manuscript, 2010. Available at[4] http://arxiv.org/pdf/1007.4652. | MR | Zbl
, and .[11] An Introduction to Statistical Analysis of Random Arrays. VSP, Utrecht, 1998. | MR | Zbl
.[12] A new application of random matrices: is not a group. Ann. of Math. (2) 162 (2005) 711-775. | MR | Zbl
and .[13] A CLT for information-theoretic statistics of non-centered Gram random matrices. Random Matrices Theory Appl. 1 (2012) 1150010. | MR | Zbl
, , and .[14] The empirical distribution of the eigenvalues of a Gram matrix with a given variance profile. Ann. Inst. Henri Poincaré Probab. Stat. 42 (2006) 649-670. | EuDML | Numdam | MR | Zbl
, and .[15] Deterministic equivalents for certain functionals of large random matrices. Ann. Appl. Probab. 17 (2007) 875-930. | MR | Zbl
, and .[16] Topics in Matrix Analysis. Cambridge Univ. Press, Cambridge, 1994. | MR | Zbl
and .[17] On the fluctuations of the mutual information for non centered MIMO channels: The non Gaussian case. In Proc. IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2010.
, , , and .[18] Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N.S.) 72 (1967) 507-536. | MR | Zbl
and .[19] Improved estimation of eigenvalues and eigenvectors of covariance matrices using their sample estimates. IEEE Trans. Inform. Theory 54 (2008) 5113-5129. | MR | Zbl
.[20] On the asymptotic behavior of the sample estimates of eigenvalues and eigenvectors of covariance matrices. IEEE Trans. Signal Process. 56 (2008) 5353-5368. | MR
.[21] Modified subspace algorithms for DOA estimation with large arrays. IEEE Trans. Signal Process. 56 (2008) 598-614. | MR
and .[22] Real and Complex Analysis, 3rd edition. McGraw-Hill, New York, 1986. | Zbl
.[23] Strong convergence of the empirical distribution of eigenvalues of large-dimensional random matrices. J. Multivariate Anal. 55 (1995) 331-339. | MR | Zbl
.[24] On the empirical distribution of eigenvalues of a class of large-dimensional random matrices. J. Multivariate Anal. 54 (1995) 175-192. | MR | Zbl
and .[25] Improved subspace estimation for multivariate observations of high dimension: The deterministic signals case. IEEE Trans. Inform. Theory 58 (2012) 1043-1068. | MR
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