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Ф. Г¨eтце, А. А. Наумов, А. Н. Тихомиров Локальный полукруговой закон при моментных условиях: преобразование Стилтьеса, жесткость и делокализация Теория вероятностей и ее применения, 2017, 62:1, 72–103

Список литературы [1] L. Arnold, “On the asymptotic distribution of the eigenvalues of random matrices”, MathSciNet Zentralblatt J. Math. Anal. Appl., 20:2 (1967), 262–268 MATH [2] Z. Bai, J. Hu, G. Pan, W. Zhou, “A note on rate of convergence in probability to semiMathSciNet circular law”, Electron. J. Probab., 16 (2011), paper № 88, 2439–2451 Zentralblatt MATH

[3] Z. Bai, J. W. Silverstein, Spectral analysis of large dimensional random matrices, 2nd MathSciNet ed., Springer Ser. Statist., Springer, New York, 2010, xvi+551 pp. Zentralblatt MATH

[4] M. Banna, F. Merlevède, M. Peligrad, “On the limiting spectral distribution for a large class of symmetric random matrices with correlated entries”, Stochastic Process. Appl., MathSciNet Zentralblatt 125:7 (2015), 2700–2726 MATH [5] C. Cacciapuoti, A. Maltsev, B. Schlein, “Bounds for the Stieltjes transform and the density of states of Wigner matrices”, Probab. Theory Related Fields, 163:1-2 (2015), MathSciNet Zentralblatt 1–59 MATH [6] Л. Эрд¨eш, “Универсальность случайных матриц Вигнера: обзор последних реMathSciNet зультатов”, Успехи матем. наук, 66:3(399) (2011), 67–198 Math-Net.Ru Zentralblatt os, “Universality of Wigner random matrices: a survey of MATH ; англ. пер.: L. Erd˝ ads recent results”, Russian Math. Surveys, 66:3 (2011), 507–626 [7] L. Erdős, A. Knowles, H.-T. Yau, J. Yin, “Spectral statistics of Erdős–Rényi graphs II: Eigenvalue spacing and the extreme eigenvalues”, Comm. Math. Phys., 314:3 (2012), MathSciNet Zentralblatt 587–640 MATH [8] L. Erdős, A. Knowles, H.-T. Yau, J. Yin, “The local semicircle law for a general class of random matrices”, Electron. J. Probab., 18 (2013), paper № 59, 58 pp. MathSciNet Zentralblatt MATH

[9] L. Erdős, A. Knowles, H.-T. Yau, J. Yin, “Spectral statistics of Erdös–Rényi graphs I: MathSciNet Zentralblatt Local semicircle law”, Ann. Probab., 41:3B (2013), 2279–2375 MATH [10] L. Erdős, B. Schlein, H.-T. Yau, “Local semicircle law and complete delocalization for MathSciNet Wigner random matrices”, Comm. Math. Phys., 287:2 (2009), 641–655 Zentralblatt MATH

[11] L. Erdős, B. Schlein, H.-T. Yau, “Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices”, Ann. Probab., 37:3 (2009), 815–852 MathSciNet Zentralblatt MATH

[12] L. Erdős, B. Schlein, H.-T. Yau, “Wegner estimate and level repulsion for Wigner MathSciNet random matrices”, Int. Math. Res. Not. IMRN, 2010:3 (2010), 436–479 Zentralblatt MATH

[13] E. Giné, R. Latała, J. Zinn, “Exponential and moment inequalities for U statistics”, High dimensional probability, V. II (Seattle, WA, 1999), Progr. Probab., 47, Birkhäuser Boston, Boston, MA, 2000, 13–38 MathSciNet Zentralblatt MATH [14] В. Л. Гирко, Теория случайных детерминантов, Вища школа, Киев, 1980, 368 с. MathSciNet Zentralblatt MATH ; англ. пер.: V. L. Girko, Theory of random determinants, Math. Appl. (Soviet Ser.), 45, Kluwer Acad. Publ., Dordrecht, 1988, xxv+677 с. Zentralblatt MATH [15] В. Л. Гирко, “Спектральная теория случайных матриц”, Успехи матем. наук, 40:1(241) (1985), 67–106 Math-Net.Ru MathSciNet Zentralblatt MATH ; англ. пер.: V. L. Girko, “Spectral theory of random matrices”, Russian Math. Surveys, 40:1 (1985), 77–120

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[16] Ф. Г¨eтце, А. А. Наумов, А. Н. Тихомиров, “Предельные теоремы для двух классов случайных матриц с зависимыми элементами”, Теория вероятн. и ее приZentralblatt мен., 59:1 (2014), 61–80 Math-Net.Ru otze, A. A. Naumov, MATH ; англ. пер.: F. G¨ A. N. Tikhomirov, “Limit theorems for two classes of random matrices with dependent entries”, Theory Probab. Appl., 59:1 (2015), 23–39 [17] F. Götze, A. Naumov, A. Tikhomirov, Local semicircle law under moment conditions. Part I: The Stieltjes transform, arXiv: 1510.07350 [18] F. Götze, A. Naumov, A. Tikhomirov, Local semicircle law under moment conditions. Part II: Localization and delocalization, arXiv: 1511.00862 [19] F. Götze, A. Tikhomirov, “Rate of convergence to the semi-circular law”, Probab. MathSciNet Zentralblatt Theory Related Fields, 127:2 (2003), 228–276 MATH [20] F. Götze, A. Tikhomirov, On the rate of convergence to the semi-circular law, arXiv: 1109.0611 [21] F. Götze, A. Tikhomirov, Rate of convergence of the empirical spectral distribution function to the semi-circular law, arXiv: 1407.2780 [22] F. Götze, A. Tikhomirov, “Optimal bounds for convergence of expected spectral distributions to the semi-circular law”, Probab. Theory Related Fields, 165:1-2 (2016), Zentralblatt 163–233 MATH [23] J. Gustavsson, “Gaussian fluctuations of eigenvalues in the GUE”, Ann. Inst. MathSciNet Zentralblatt H. Poincaré Probab. Statist., 41:2 (2005), 151–178 MATH [24] J. O. Lee, J. Yin, “A necessary and sufficient condition for edge universality of Wigner MathSciNet Zentralblatt matrices”, Duke Math. J., 163:1 (2014), 117–173 MATH [25] А. А. Наумов, “Предельные теоремы для двух классов случайных матриц с гауссовскими элементами”, Вероятность и статистика. 19, Зап. науч. сем. ПОМИ, 412, ПОМИ, СПб., 2013, 215–226 Math-Net.Ru MathSciNet Zentralblatt MATH ; англ. пер.: A. A. Naumov, “Limit theorems for two classes of random matrices with Gaussian entries”, J. Math. Sci. (N. Y.), 204:1 (2015), 140–147 [26] Л. А. Пастур, “Спектры случайных самосопряженных операторов”, Успехи матем. наук, 28:1(169) (1973), 3–64 Math-Net.Ru MathSciNet Zentralblatt англ. пер.: MATH ; L. A. Pastur, “Spectra of random self adjoint operators”, Russian Math. Surveys, 28:1 (1973), 1–67 [27] D. Shlyakhtenko, “Random Gaussian band matrices and freeness with amalgamation”, MathSciNet Zentralblatt Internat. Math. Res. Notices, 1996:20 (1996), 1013–1025 MATH [28] Terence Tao, Van Vu, “Random matrices: the universality phenomenon for Wigner ensembles”, Modern aspects of random matrix theory, Proc. Sympos. Appl. Math., 72, MathSciNet Zentralblatt Amer. Math. Soc., Providence, RI, 2014, 121–172 MATH ; arXiv: 1202.0068 [29] Terence Tao, Van Vu, “Random matrices: sharp concentration of eigenvalues”, RanMathSciNet Zentralblatt dom Matrices Theory Appl., 2:3 (2013), 1350007, 31 pp. MATH