Limit theorems for two classes of random matrices with dependent entries
Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 1, pp. 61-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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F. Götze; A. A. Naumov; A. N. Tikhomirov. Limit theorems for two classes of random matrices with dependent entries. Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 1, pp. 61-80. http://geodesic.mathdoc.fr/item/TVP_2014_59_1_a3/

[1] Wigner E. P., “On the distribution of the roots of certain symmetric matrices”, Ann. Math., 67 (1958), 325–327 | DOI | MR | Zbl

[2] Arnold L., “On {W}igner's semicircle law for the eigenvalues of random matrices”, Z. Wahrscheinlichkeitstheor. verw. Geb., 19 (1971), 191–198 | DOI | MR

[3] Pastur L. A., “Spektry sluchainykh samosopryazhennykh operatorov”, Uspekhi matem. nauk, 28:1 (1973), 3–64 | MR | Zbl

[4] Shlyakhtenko D., “Random gaussian band matrices and freeness with amalgamation”, Int. Math. Res. Not., 1996, no. 20, 1013–1025 | DOI | MR | Zbl

[5] Erdős L., Universality of Wigner random matrices: a survey of recent results, arXiv: 1004.0861

[6] Götze F., Tikhomirov A. N., “Limit theorems for spectra of random matrices with martingale structure”, Teoriya veroyatn. i ee primen., 51:1 (2006), 171–192 | DOI | MR

[7] Hall P., Heyde C. C., Martingale Limit Theory and Its Application, Academic Press, New York, 1980, 308 pp. | MR

[8] Rosenzweig N., Statistical Mechanics of Equally Likely Quantum Systems, Benjamin, New York, 1963, 91 pp. | MR | Zbl

[9] Bronk B. V., Topics in the theory of random matrices, PhD thesis, Princeton Univ., Princeton, 1964

[10] Naumov A. A., “Predelnye teoremy dlya dvukh klassov sluchainykh matrits s gaussovskimi elementami”, Zap. nauch. sem. POMI, 412, 2013, 214–225 | MR

[11] Wishart J., “Generalised product moment distribution in samples from a normal multivariate population”, Biometrika, 20 (1928), 32–52 | DOI | MR | Zbl

[12] Marchenko V. A., Pastur L. A., “Raspredelenie sobstvennykh znachenii v nekotorykh ansamblyakh sluchainykh matrits”, Matem. sb., 72:4 (1967), 507–536 | Zbl

[13] O'Rourke S., “A note on the Marchenko–Pastur law for a class of random matrices with dependent entries”, Electron. Commun. Probab., 17 (2012), 28, 13 pp. | MR

[14] Götze F., Tikhomirov A. N., “Limit theorems for spectra of positive random matrices under dependence”, Zap. nauch. sem. POMI, 311, 2004, 92–123 | MR

[15] Adamczak R., “On the {M}archenko–{P}astur and circular laws for some classes of random matrices with dependent entries”, Electron. J. Probab., 16:37 (2011), 1068–1095 | MR

[16] Bentkus V., “Novyi podkhod k approksimatsiyam v teorii veroyatnostei i teorii operatorov”, Liet. Mat. Rink., 43:4 (2003), 444–470 | MR | Zbl

[17] Pastur L., Shcherbina M., Eigenvalue Distribution of Large Random Matrices, Amer. Math. Soc., Providence, 2011, 632 pp. | MR | Zbl

[18] Bai Z., Silverstein J. W., Spectral Analysis of Large Dimensional Random Matrices, Springer, Dordrecht, 2010, 551 pp. | MR