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References

  • Anderson, Greg W.; Zeitouni, Ofer. A CLT for a band matrix model. Probab. Theory Related Fields 134 (2006), no. 2, 283--338. MR2222385
  • Bai, Z. D. Methodologies in spectral analysis of large-dimensional random matrices, a review. With comments by G. J. Rodgers and Jack W. Silverstein; and a rejoinder by the author. Statist. Sinica 9 (1999), no. 3, 611--677. MR1711663
  • Bai, Z., Silverstein, J. W. : Spectral analysis of large dimensional random matrices. Science Press, Beijing, 2006
  • Basak, Anirban; Bose, Arup. Limiting spectral distributions of some band matrices. Period. Math. Hungar. 63 (2011), no. 1, 113--150. MR2853175
  • Basor, Estelle L. Toeplitz determinants, Fisher-Hartwig symbols, and random matrices. Recent perspectives in random matrix theory and number theory, 309--336, London Math. Soc. Lecture Note Ser., 322, Cambridge Univ. Press, Cambridge, 2005. MR2166467
  • Bose, Arup; Chatterjee, Sourav; Gangopadhyay, Sreela. Limiting spectral distributions of large dimensional random matrices. J. Indian Statist. Assoc. 41 (2003), no. 2, 221--259. MR2101995
  • Bose, Arup; Mitra, Joydip. Limiting spectral distribution of a special circulant. Statist. Probab. Lett. 60 (2002), no. 1, 111--120. MR1945684
  • 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
  • Chatterjee, Sourav. Fluctuations of eigenvalues and second order Poincaré inequalities. Probab. Theory Related Fields 143 (2009), no. 1-2, 1--40. MR2449121
  • Diaconis, Persi. Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture. Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 2, 155--178. MR1962294
  • Diaconis, Persi; Evans, Steven N. Linear functionals of eigenvalues of random matrices. Trans. Amer. Math. Soc. 353 (2001), no. 7, 2615--2633. MR1828463
  • Diaconis, Persi; Shahshahani, Mehrdad. On the eigenvalues of random matrices. Studies in applied probability. J. Appl. Probab. 31A (1994), 49--62. MR1274717
  • Dumitriu, Ioana; Edelman, Alan. Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models. J. Math. Phys. 47 (2006), no. 6, 063302, 36 pp. MR2239975
  • Grenander, Ulf; Szegö, Gabor. Toeplitz forms and their applications. California Monographs in Mathematical Sciences University of California Press, Berkeley-Los Angeles 1958 vii+245 pp. MR0094840
  • 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
  • Johansson, Kurt. On Szegő's asymptotic formula for Toeplitz determinants and generalizations. Bull. Sci. Math. (2) 112 (1988), no. 3, 257--304. MR0975365
  • Johansson, Kurt. On fluctuations of eigenvalues of random Hermitian matrices. Duke Math. J. 91 (1998), no. 1, 151--204. MR1487983
  • Jonsson, Dag. Some limit theorems for the eigenvalues of a sample covariance matrix. J. Multivariate Anal. 12 (1982), no. 1, 1--38. MR0650926
  • Kargin, Vladislav. Spectrum of random Toeplitz matrices with band structure. Electron. Commun. Probab. 14 (2009), 412--421. MR2551851
  • Horn, Roger A.; Johnson, Charles R. Matrix analysis. Cambridge University Press, Cambridge, 1985. xiii+561 pp. ISBN: 0-521-30586-1 MR0832183
  • Liu, Dang-Zheng; Wang, Zheng-Dong. Limit distribution of eigenvalues for random Hankel and Toeplitz band matrices. J. Theoret. Probab. 24 (2011), no. 4, 988--1001. MR2851241
  • Massey, Adam; Miller, Steven J.; Sinsheimer, John. Distribution of eigenvalues of real symmetric palindromic Toeplitz matrices and circulant matrices. J. Theoret. Probab. 20 (2007), no. 3, 637--662. MR2337145
  • Popescu, Ionel. General tridiagonal random matrix models, limiting distributions and fluctuations. Probab. Theory Related Fields 144 (2009), no. 1-2, 179--220. MR2480789
  • Sen, Arnab; Virág, Bálint. Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix. Electron. Commun. Probab. 16 (2011), 706--711. MR2861434
  • Sen, A. and Virág, B.: The top eigenvalue of the random Toeplitz matrix and the Sine kernel, arXiv:1109.5494.
  • Sinai, Ya.; Soshnikov, A. Central limit theorem for traces of large random symmetric matrices with independent matrix elements. Bol. Soc. Brasil. Mat. (N.S.) 29 (1998), no. 1, 1--24. MR1620151


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