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References

  1. Bai, Z. D.; Silverstein, Jack W. CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Probab. 32 (2004), no. 1A, 553--605. MR2040792 (2005b:60046)

  2. Baik, Jinho; Silverstein, Jack W. Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97 (2006), no. 6, 1382--1408. MR2279680 (2008a:60063)

  3. Bercovici, Hari; Pata, Vittorino. Limit laws for products of free and independent random variables. Studia Math. 141 (2000), no. 1, 43--52. MR1782911 (2001i:46105)

  4. Bercovici, Hari; Voiculescu, Dan. Free convolution of measures with unbounded support. Indiana Univ. Math. J. 42 (1993), no. 3, 733--773. MR1254116 (95c:46109)

  5. Borade, Shashibhushan; Zheng, Lizhong; Gallager, Robert. Amplify-and-forward in wireless relay networks: rate, diversity, and network size. IEEE Trans. Inform. Theory 53 (2007), no. 10, 3302--3318. MR2419789 (2009g:94002)

  6. Brown, L. G. Lidski?'s theorem in the type ${rm II}$ case. Geometric methods in operator algebras (Kyoto, 1983), 1--35, Pitman Res. Notes Math. Ser., 123, Longman Sci. Tech., Harlow, 1986. MR0866489 (88d:47024)

  7. Crisanti, A.; Paladin, G.; Vulpiani, A. Products of random matrices in statistical physics. With a foreword by Giorgio Parisi. Springer Series in Solid-State Sciences, 104. Springer-Verlag, Berlin, 1993. xiv+166 pp. ISBN: 3-540-56575-2 MR1278483 (95d:82031)

  8. Furstenberg, H.; Kesten, H. Products of random matrices. Ann. Math. Statist. 31 1960 457--469. MR0121828 (22 #12558)

  9. Gill, Richard D.; Johansen, S¯ren. A survey of product-integration with a view toward application in survival analysis. Ann. Statist. 18 (1990), no. 4, 1501--1555. MR1074422 (92f:60125)

  10. Haagerup, Uffe; Larsen, Flemming. Brown's spectral distribution measure for $R$-diagonal elements in finite von Neumann algebras. J. Funct. Anal. 176 (2000), no. 2, 331--367. MR1784419 (2001i:46106)

  11. Haagerup, Uffe; Schultz, Hanne. Invariant subspaces for operators in a general ${rm II}sb 1$-factor. Publ. Math. Inst. Hautes ?tudes Sci. No. 109 (2009), 19--111. MR2511586 (2010e:47020)

  12. Isopi, Marco; Newman, Charles M. The triangle law for Lyapunov exponents of large random matrices. Comm. Math. Phys. 143 (1992), no. 3, 591--598. MR1145601 (93d:60045)

  13. Kargin, Vladislav. The norm of products of free random variables. Probab. Theory Related Fields 139 (2007), no. 3-4, 397--413. MR2322702 (2008g:46117)

  14. Kargin, Vladislav. Lyapunov exponents of free operators. J. Funct. Anal. 255 (2008), no. 8, 1874--1888. MR2462579 (2009k:46122)

  15. Newman, C. M. Lyapunov exponents for some products of random matrices: exact expressions and asymptotic distributions. Random matrices and their applications (Brunswick, Maine, 1984), 121--141, Contemp. Math., 50, Amer. Math. Soc., Providence, RI, 1986. MR0841087 (88a:60020)

  16. Newman, Charles M. The distribution of Lyapunov exponents: exact results for random matrices. Comm. Math. Phys. 103 (1986), no. 1, 121--126. MR0826860 (87h:60119)

  17. Nica, Alexandru; Speicher, Roland. $R$-diagonal pairsa common approach to Haar unitaries and circular elements. Free probability theory (Waterloo, ON, 1995), 149--188, Fields Inst. Commun., 12, Amer. Math. Soc., Providence, RI, 1997. MR1426839 (98b:46083)

  18. Oseledec, V. I. A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems. (Russian) Trudy Moskov. Mat. Oböč. 19 1968 179--210. MR0240280 (39 #1629)

  19. Ratnarajah, T.; Vaillancourt, R.; Alvo, M. Complex random matrices and Rayleigh channel capacity. Commun. Inf. Syst. 3 (2003), no. 2, 119--138. MR2042593 (2005b:94016)

  20. Rider, B.; Silverstein, Jack W. Gaussian fluctuations for non-Hermitian random matrix ensembles. Ann. Probab. 34 (2006), no. 6, 2118--2143. MR2294978 (2008d:60036)

  21. Ruelle, David. Characteristic exponents and invariant manifolds in Hilbert space. Ann. of Math. (2) 115 (1982), no. 2, 243--290. MR0647807 (83j:58097)

  22. Verdu. S and Tulino A.M., Random Matrix Theory and Wireless Communications, Now Publishers Inc., 2004.

  23. Voiculescu D. Free Probability Theory, Fields Institute Communications, 1997 .

  24. Voiculescu, D. V.; Dykema, K. J.; Nica, A. Free random variables. A noncommutative probability approach to free products with applications to random matrices, operator algebras and harmonic analysis on free groups. CRM Monograph Series, 1. American Mathematical Society, Providence, RI, 1992. vi+70 pp. ISBN: 0-8218-6999-X MR1217253 (94c:46133)



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