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We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum.
von Neumann, JohnJ. andGoldstine, H. H.H. H. (1947). Numerical inverting of matrices of high order. Bull. Amer. Math. Soc. 53 1021–1099
1947
Earlier work this paper cites.
Goldstine, Herman H.H. H. andvon Neumann, JohnJ. (1951). Numerical inverting of matrices of high order. II. Proc. Amer. Math. Soc. 2 188–202
1951
Earlier work this paper cites.
Erdélyi, ArthurA., Magnus, WilhelmW., Oberhettinger, FritzF. andTricomi, Francesco G.F. G. (1953). Higher Transcendental Functions. Vols. I, II. McGraw-Hill Book Co., New York
1953
Earlier work this paper cites.
Loubaton, PhilippeP. andVallet, PascalP. (2011). Almost sure localization of the eigenvalues in a Gaussian information plus noise model—application to the spiked models. Electron. J. Probab. 16 1934–1959
1959
Earlier work this paper cites.
Marčenko, V. A.V. A. andPastur, L. A.L. A. (1967). Distribution of eigenvalues in certain sets of random matrices. Mat. Sb. (N.S.) 72 (114) 507–536
1967
Earlier work this paper cites.
Olver, F. W. J.F. W. J. (1974). Asymptotics and Special Functions. Computer Science and Applied Mathematics. Academic Press, New York
1974
Earlier work this paper cites.
Geman, StuartS. (1980). A limit theorem for the norm of random matrices. Ann. Probab. 8 252–261
1980
Earlier work this paper cites.
Rudin, WalterW. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill Book Co., New York
1987
Earlier work this paper cites.
Edelman, AlanA. (1988). Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Appl. 9 543–560
1988
Earlier work this paper cites.
Voiculescu, DanD. (1991). Limit laws for random matrices and free products. Invent. Math. 104 201–220
1991
Earlier work this paper cites.
Bai, Z. D.Z. D. andYin, Y. Q.Y. Q. (1993). Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Probab. 21 1275–1294
1993
Earlier work this paper cites.
Forrester, P. J.P. J. (1993). The spectrum edge of random matrix ensembles. Nuclear Phys. B 402 709–728
1993
Earlier work this paper cites.
Tracy, Craig A.C. A. andWidom, HaroldH. (1994). Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 151–174
1994
Earlier work this paper cites.
Tracy, Craig A.C. A. andWidom, HaroldH. (1994). Level spacing distributions and the Bessel kernel. Comm. Math. Phys. 161 289–309
1994
Earlier work this paper cites.
Silverstein, Jack W.J. W. (1995). Strong convergence of the empirical distribution of eigenvalues of large-dimensional random matrices. J. Multivariate Anal. 55 331–339
1995
Earlier work this paper cites.
Silverstein, Jack W.J. W. andChoi, Sang-IlS.-I. (1995). Analysis of the limiting spectral distribution of large-dimensional random matrices. J. Multivariate Anal. 54 295–309
1995
Earlier work this paper cites.
Saff, Edward B.E. B. andTotik, VilmosV. (1997). Logarithmic Potentials with External Fields. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 316. Springer, Berlin
1997
Earlier work this paper cites.
Bai, Z. D.Z. D. andSilverstein, Jack W.J. W. (1998). No eigenvalues outside the support of the limiting spectral distribution of large-dimensional sample covariance matrices. Ann. Probab. 26 316–345
1998
Earlier work this paper cites.
Brézin, E.E. andHikami, S.S. (1998). Universal singularity at the closure of a gap in a random matrix theory. Phys. Rev. E (3) 57 4140–4149
1998
Earlier work this paper cites.
van der Vaart, A. W.A. W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics 3. Cambridge Univ. Press, Cambridge
1998
Earlier work this paper cites.
Bai, Z. D.Z. D. andSilverstein, Jack W.J. W. (1999). Exact separation of eigenvalues of large-dimensional sample covariance matrices. Ann. Probab. 27 1536–1555
1999
Earlier work this paper cites.
Laloux, L.L., P., CizeauC., Bouchaud, J.-P.J.-P. andPotters, M.M. (1999). Noise dressing of financial correlation matrices. Phys. Rev. Lett. 83 1467
1999
Earlier work this paper cites.
Gohberg, IsraelI., Goldberg, SeymourS. andKrupnik, NahumN. (2000). Traces and Determinants of Linear Operators. Operator Theory: Advances and Applications 116. Birkhäuser, Basel
2000
Earlier work this paper cites.
Johansson, KurtK. (2000). Shape fluctuations and random matrices. Comm. Math. Phys. 209 437–476
2000
Earlier work this paper cites.
Johnstone, Iain M.I. M. (2001). On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 295–327
2001
Cited alongside, same era.
Soshnikov, AlexanderA. (2002). A note on universality of the distribution of the largest eigenvalues in certain sample covariance matrices. J. Stat. Phys. 108 1033–1056
2002
Cited alongside, same era.
Borodin, AlexeiA. andForrester, Peter J.P. J. (2003). Increasing subsequences and the hard-to-soft edge transition in matrix ensembles. J. Phys. A 36 2963–2981
2003
Cited alongside, same era.
Bai, Z. D.Z. D. andSilverstein, Jack W.J. W. (2004). CLT for linear spectral statistics of large-dimensional sample covariance matrices. Ann. Probab. 32 553–605
2004
Cited alongside, same era.
Baik, JinhoJ., Ben Arous, GérardG. andPéché, SandrineS. (2005). Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 1643–1697
Tao, TerenceT. andVu, VanV. (2010). Random matrices: The distribution of the smallest singular values. Geom. Funct. Anal. 20 260–297
2010
Later among the works it cites.
Benaych-Georges, F.F., Guionnet, A.A. andMaida, M.M. (2011). Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices. Electron. J. Probab. 16 1621–1662
2011
Later among the works it cites.
Benaych-Georges, FlorentF. andNadakuditi, Raj RaoR. R. (2011). The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. Adv. Math. 227 494–521
2011
Later among the works it cites.
Bianchi, P.P., Debbah, M.M., Maida, M.M. andNajim, J.J. (2011). Performance of statistical tests for single-source detection using random matrix theory. IEEE Trans. Inform. Theory 57 2400–2419
2011
Later among the works it cites.
Bloemendal, A.A. andVirág, B.B. (2011). Limits of spiked random matrices II. Unpublished manuscript
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2005
Cited alongside, same era.
Ben Arous, G.G. andPéché, S.S. (2005). Universality of local eigenvalue statistics for some sample covariance matrices. Comm. Pure Appl. Math. 58 1316–1357
2005
Cited alongside, same era.
Simon, BarryB. (2005). Trace Ideals and Their Applications, 2nd ed. Mathematical Surveys and Monographs 120. Amer. Math. Soc., Providence, RI
2005
Cited alongside, same era.
Baik, JinhoJ. andSilverstein, Jack W.J. W. (2006). Eigenvalues of large sample covariance matrices of spiked population models. J. Multivariate Anal. 97 1382–1408
2006
Cited alongside, same era.
Péché, S.S. (2006). The largest eigenvalue of small rank perturbations of Hermitian random matrices. Probab. Theory Related Fields 134 127–173
2006
Cited alongside, same era.
Davies, E. BrianE. B. (2007). Linear Operators and Their Spectra. Cambridge Studies in Advanced Mathematics 106. Cambridge Univ. Press, Cambridge
2007
Cited alongside, same era.
El Karoui, NoureddineN. (2007). Tracy–Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices. Ann. Probab. 35 663–714
2007
Cited alongside, same era.
Bai, ZhidongZ. andYao, Jian-fengJ.-f. (2008). Central limit theorems for eigenvalues in a spiked population model. Ann. Inst. Henri Poincaré Probab. Stat. 44 447–474
2008
Cited alongside, same era.
2011
Later among the works it cites.
Couillet, RomainR. andDebbah, MérouaneM. (2011). Random Matrix Methods for Wireless Communications. Cambridge Univ. Press, Cambridge
2011
Later among the works it cites.
Kuijlaars, A. B. J.A. B. J. (2011). Universality. In The Oxford handbook of random matrix theory (G.G. Akemann, J.J. Baik andP.P. Di Francesco, eds.) 103–134. Oxford Univ. Press, Oxford
2011
Later among the works it cites.
Pastur, LeonidL. andShcherbina, MariyaM. (2011). Eigenvalue Distribution of Large Random Matrices. Mathematical Surveys and Monographs 171. Amer. Math. Soc., Providence, RI
2011
Later among the works it cites.
Basor, EstelleE., Chen, YangY. andZhang, LunL. (2012). PDEs satisfied by extreme eigenvalues distributions of GUE and LUE. Random Matrices Theory Appl. 1 1150003, 21
2012
Later among the works it cites.
Mo, M. Y.M. Y. (2012). Rank 1 real Wishart spiked model. Comm. Pure Appl. Math. 65 1528–1638
2012
Later among the works it cites.
Wang, KeK. (2012). Random covariance matrices: Universality of local statistics of eigenvalues up to the edge. Random Matrices Theory Appl. 1 1150005, 24
2012
Later among the works it cites.
Bloemendal, AlexA. andVirág, BálintB. (2013). Limits of spiked random matrices I. Probab. Theory Related Fields 156 795–825
2013
Later among the works it cites.
Girotti, M.M. (2013). Riemann–Hilbert approach to gap probabilities for the Bessel process. Preprint
2013
Later among the works it cites.
2013
Later among the works it cites.
Bleher, Pavel M.P. M. andKuijlaars, Arno B. J.A. B. J. (2005). Integral representations for multiple Hermite and multiple Laguerre polynomials. Ann. Inst. Fourier (Grenoble) 55 2001–2014
2014
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2014
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2014
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Knowles, A.A. andYin, J.J. (2014). Anisotropic local laws for random matrices. Preprint
2014
Closest in time.
2014
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Münnix, Michael C.M. C., Schäfer, RudiR. andGuhr, ThomasT. (2014). A random matrix approach to credit risk. PLoS ONE 9 e98030
2014
Closest in time.
Pillai, Natesh S.N. S. andYin, JunJ. (2014). Universality of covariance matrices. Ann. Appl. Probab. 24 935–1001
2014
Closest in time.
Bao, Z.Z., Pan, G.G. andZhou, W.W. (2015). Universality for the largest eigenvalue of sample covariance matrices with general population. Ann. Statist. 43 382–421
2015
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