References

• 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
• Bai, Zhidong; Yao, Jian-feng. Central limit theorems for eigenvalues in a spiked population model. Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), no. 3, 447--474. MR2451053
• Baik, Jinho; Ben Arous, Gérard; Péché, Sandrine. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 (2005), no. 5, 1643--1697. MR2165575
• 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
• 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
• Benaych-Georges, Florent; Nadakuditi, Raj Rao. The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Adv. Math. 227 (2011), no. 1, 494--521. MR2782201
• 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. Central limit theorems for eigenvalues of deformations of Wigner matrices. Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012), no. 1, 107--133. MR2919200
• de Jong, Peter. A central limit theorem for generalized quadratic forms. Probab. Theory Related Fields 75 (1987), no. 2, 261--277. MR0885466
• Fox, Robert; Taqqu, Murad S. Central limit theorems for quadratic forms in random variables having long-range dependence. Probab. Theory Related Fields 74 (1987), no. 2, 213--240. MR0871252
• Hachem, Walid; Loubaton, Philippe; Najim, Jamal; Vallet, Pascal. On bilinear forms based on the resolvent of large random matrices. Ann. Inst. Henri Poincaré Probab. Stat. 49 (2013), no. 1, 36--63. MR3060147
• Yakubovskiĭ, A.; Memen, Zh. Functional central limit theorems for a class of quadratic forms in independent random variables. (Russian) Teor. Veroyatnost. i Primenen. 38 (1993), no. 3, 600--612; translation in Theory Probab. Appl. 38 (1993), no. 3, 423--432 MR1404667
• Johnstone, Iain M. On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 (2001), no. 2, 295--327. MR1863961
• Knowles, Antti; Yin, Jun. The outliers of a deformed Wigner matrix. Ann. Probab. 42 (2014), no. 5, 1980--2031. MR3262497
• Lee, Seunggeun; Zou, Fei; Wright, Fred A. Convergence and prediction of principal component scores in high-dimensional settings. Ann. Statist. 38 (2010), no. 6, 3605--3629. MR2766862
• Marcenko, V.A. and Pastur, L.A. (1967). Distribution of eigenvalues for some sets of random matrices. Math. USSR-Sb, 1, 457--483.
• Mikosch, T. Functional limit theorems for random quadratic forms. Stochastic Process. Appl. 37 (1991), no. 1, 81--98. MR1091696
• Pan, Guangming; Miao, Baiqi; Jin, Baisuo. Central limit theorem of random quadratics forms involving random matrices. Statist. Probab. Lett. 78 (2008), no. 6, 804--809. MR2409545
• Paul, Debashis. Asymptotics of sample eigenstructure for a large dimensional spiked covariance model. Statist. Sinica 17 (2007), no. 4, 1617--1642. MR2399865
• Pizzo, Alessandro; Renfrew, David; Soshnikov, Alexander. On finite rank deformations of Wigner matrices. Ann. Inst. Henri Poincaré Probab. Stat. 49 (2013), no. 1, 64--94. MR3060148
• Rotarʹ, V. I. Certain limit theorems for polynomials of degree two. (Russian) Teor. Verojatnost. i Primenen. 18 (1973), 527--534. MR0326803
• Renfrew, David; Soshnikov, Alexander. On finite rank deformations of Wigner matrices II: Delocalized perturbations. Random Matrices Theory Appl. 2 (2013), no. 1, 1250015, 36 pp. MR3039820
• Sevastyanov, B.A. (1961). A class of limit distributions for quadratic forms of normal stochastic variables. Theor. Probab. Appl., 6, 337--340.
• Whittle, P. On the convergence to normality of quadratic forms in independent variables. Teor. Verojatnost. i Primenen. 9 1964 113--118. MR0161429