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  • Anderson, Greg W.; Guionnet, Alice; Zeitouni, Ofer. An introduction to random matrices. Cambridge Studies in Advanced Mathematics, 118. Cambridge University Press, Cambridge, 2010. xiv+492 pp. ISBN: 978-0-521-19452-5 MR2760897
  • Bai, Zhidong; Silverstein, Jack W. Spectral analysis of large dimensional random matrices. Second edition. Springer Series in Statistics. Springer, New York, 2010. xvi+551 pp. ISBN: 978-1-4419-0660-1 MR2567175
  • S. Banerjee and A. Bose. Noncrossing partitions, Catalan words and the semicircular law. To appear in J. Theoret. Probab., 2011. URL rl
  • Benaych-Georges, Florent. Rectangular random matrices, entropy, and Fisher's information. J. Operator Theory 62 (2009), no. 2, 371--419. MR2552088
  • Benaych-Georges, Florent. Rectangular random matrices, related convolution. Probab. Theory Related Fields 144 (2009), no. 3-4, 471--515. MR2496440
  • Benaych-Georges, F.; Guionnet, A.; Maida, M. Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices. Electron. J. Probab. 16 (2011), no. 60, 1621--1662. MR2835249
  • Biane, Philippe. On the free convolution with a semi-circular distribution. Indiana Univ. Math. J. 46 (1997), no. 3, 705--718. MR1488333
  • Bose, Arup; Sen, Arnab. Another look at the moment method for large dimensional random matrices. Electron. J. Probab. 13 (2008), no. 21, 588--628. MR2399292
  • Bose, Arup; Hazra, Rajat Subhra; Saha, Koushik. Convergence of joint moments for independent random patterned matrices. Ann. Probab. 39 (2011), no. 4, 1607--1620. MR2857252
  • Bose, Arup; Subhra Hazra, Rajat; Saha, Koushik. Half independence and half cumulants. Electron. Commun. Probab. 16 (2011), 405--422. MR2831080
  • Bryc, Włodzimierz; Dembo, Amir; Jiang, Tiefeng. Spectral measure of large random Hankel, Markov and Toeplitz matrices. Ann. Probab. 34 (2006), no. 1, 1--38. MR2206341
  • Capitaine, Mireille; Donati-Martin, Catherine; Féral, Delphine. The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations. Ann. Probab. 37 (2009), no. 1, 1--47. MR2489158
  • Capitaine, M.; Donati-Martin, C.; Féral, D.; Février, M. Free convolution with a semicircular distribution and eigenvalues of spiked deformations of Wigner matrices. Electron. J. Probab. 16 (2011), no. 64, 1750--1792. MR2835253
  • Capitaine, M.; Casalis, M. Asymptotic freeness by generalized moments for Gaussian and Wishart matrices. Application to beta random matrices. Indiana Univ. Math. J. 53 (2004), no. 2, 397--431. MR2060040
  • Capitaine, M.; Donati-Martin, C. Strong asymptotic freeness for Wigner and Wishart matrices. Indiana Univ. Math. J. 56 (2007), no. 2, 767--803. MR2317545
  • Collins, Benoît. Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability. Int. Math. Res. Not. 2003, no. 17, 953--982. MR1959915
  • B. Collins and P. 'Sniady. Integration with respect to the Haar measure on unitary, orthogonal and symplectic group. Comm. Math. Phys., 264penalty0 (3):penalty0 773--795, 2006. ISSN 0010-3616. doi10.1007/s00220-006-1554-3. URL rl
  • Collins, Benoît; Guionnet, Alice; Maurel-Segala, Edouard. Asymptotics of unitary and orthogonal matrix integrals. Adv. Math. 222 (2009), no. 1, 172--215. MR2531371
  • Couillet, Romain; Debbah, Mérouane; Silverstein, Jack W. A deterministic equivalent for the analysis of correlated MIMO multiple access channels. IEEE Trans. Inform. Theory 57 (2011), no. 6, 3493--3514. MR2817033
  • Dykema, Ken. On certain free product factors via an extended matrix model. J. Funct. Anal. 112 (1993), no. 1, 31--60. MR1207936
  • D. Féral and S. Péché. The largest eigenvalue of rank one deformation of large Wigner matrices. Comm. Math. Phys., 272penalty0 (1):penalty0 185--228, 2007. ISSN 0010-3616. doi10.1007/s00220-007-0209-3. URL rl
  • Fulton, William. Eigenvalues of sums of Hermitian matrices (after A. Klyachko). Séminaire Bourbaki. Vol. 1997/98. Astérisque No. 252 (1998), Exp. No. 845, 5, 255--269. MR1685640
  • Hammond, Christopher; Miller, Steven J. Distribution of eigenvalues for the ensemble of real symmetric Toeplitz matrices. J. Theoret. Probab. 18 (2005), no. 3, 537--566. MR2167641
  • Hiai, Fumio; Petz, Dénes. Asymptotic freeness almost everywhere for random matrices. Acta Sci. Math. (Szeged) 66 (2000), no. 3-4, 809--834. MR1804226
  • Hiai, Fumio; Petz, Dénes. The semicircle law, free random variables and entropy. Mathematical Surveys and Monographs, 77. American Mathematical Society, Providence, RI, 2000. x+376 pp. ISBN: 0-8218-2081-8 MR1746976
  • C. Male. The norm of polynomials in large random and deterministic matrices. To appear in Prob. Theory Related Fields. 2012.
  • Nica, Alexandru; Speicher, Roland. Lectures on the combinatorics of free probability. London Mathematical Society Lecture Note Series, 335. Cambridge University Press, Cambridge, 2006. xvi+417 pp. ISBN: 978-0-521-85852-6; 0-521-85852-6 MR2266879
  • Oraby, Tamer. The spectral laws of Hermitian block-matrices with large random blocks. Electron. Comm. Probab. 12 (2007), 465--476. MR2365648
  • S. Péché. The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Related Fields, 134penalty0 (1):penalty0 127--173, 2006. ISSN 0178-8051. doi10.1007/s00440-005-0466-z. URL rl
  • Pastur, L.; Vasilchuk, V. On the law of addition of random matrices. Comm. Math. Phys. 214 (2000), no. 2, 249--286. MR1796022
  • Rashidi Far, Reza; Oraby, Tamer; Bryc, Wlodek; Speicher, Roland. On slow-fading MIMO systems with nonseparable correlation. IEEE Trans. Inform. Theory 54 (2008), no. 2, 544--553. MR2444540
  • Ryan, Øyvind. On the limit distributions of random matrices with independent or free entries. Comm. Math. Phys. 193 (1998), no. 3, 595--626. MR1624843
  • Schultz, Hanne. Non-commutative polynomials of independent Gaussian random matrices. The real and symplectic cases. Probab. Theory Related Fields 131 (2005), no. 2, 261--309. MR2117954
  • Shlyakhtenko, Dimitri. Random Gaussian band matrices and freeness with amalgamation. Internat. Math. Res. Notices 1996, no. 20, 1013--1025. MR1422374
  • Speicher, Roland. On universal products. Free probability theory (Waterloo, ON, 1995), 257--266, Fields Inst. Commun., 12, Amer. Math. Soc., Providence, RI, 1997. MR1426844
  • Speicher, Roland. Combinatorial theory of the free product with amalgamation and operator-valued free probability theory. Mem. Amer. Math. Soc. 132 (1998), no. 627, x+88 pp. MR1407898
  • Speicher, Roland. Free probability theory. The Oxford handbook of random matrix theory (2011). Oxford Univ. Press. 452--470. MR2932642
  • A. M. Tulino and S. Verd'u. Random matrices and wireless communications, volume vol. 1 of Fundations and Trends in Communications and Information Theory. Now Publishers Inc., 2004.
  • Voiculescu, Dan. Addition of certain noncommuting random variables. J. Funct. Anal. 66 (1986), no. 3, 323--346. MR0839105
  • Voiculescu, Dan. Limit laws for random matrices and free products. Invent. Math. 104 (1991), no. 1, 201--220. MR1094052
  • Voiculescu, Dan. A strengthened asymptotic freeness result for random matrices with applications to free entropy. Internat. Math. Res. Notices 1998, no. 1, 41--63. MR1601878
  • Wigner, Eugene P. On the distribution of the roots of certain symmetric matrices. Ann. of Math. (2) 67 1958 325--327. MR0095527

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