-
1
-
-
65349112203
-
An Introduction to Random Matrices
-
Cambridge University Press, New York
-
G. W. Anderson, A. Guionnet and Zeitouni O, An Introduction to Random Matrices, Cambridge Studies in Advanced Mathematics, Vol. 118 (Cambridge University Press, New York, 2010).
-
(2010)
Cambridge Studies in Advanced Mathematics
, vol.118
-
-
Anderson, G.W.1
Guionnet, A.2
Zeitouni, O.3
-
2
-
-
0347989448
-
Methodologies in spectral analysis of large-dimensional random matrices, a review
-
Z. D. Bai, Methodologies in spectral analysis of large-dimensional random matrices, a review, Statist. Sinica 9 (1999) 611-677.
-
(1999)
Statist Sinica
, vol.9
, pp. 611-677
-
-
Bai, Z.D.1
-
3
-
-
84855864044
-
Limiting behavior of eigenvectors of large Wigner matrices
-
Z. D. Bai and G. M. Pan, Limiting behavior of eigenvectors of large Wigner matrices, J. Statist. Phys. 146(3) (2012) 519-549.
-
(2012)
J Statist. Phys.
, vol.146
, Issue.3
, pp. 519-549
-
-
Bai, Z.D.1
Pan, G.M.2
-
4
-
-
27644476898
-
Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
-
J. Baik, G. Ben Arous and S. Péché, Phase transition of the largest eigenvalue for non-null complex sample covariance matrices, Ann. Probab. 33 (2005) 1643-1697.
-
(2005)
Ann. Probab.
, vol.33
, pp. 1643-1697
-
-
Baik, J.1
Ben Arous, G.2
Péché, S.3
-
5
-
-
33646507506
-
Eigenvalues of large sample covariance matrices of spiked population models
-
J. Baik and J. W. Silverstein, Eigenvalues of large sample covariance matrices of spiked population models, J. Multi. Anal. 97 (2006) 1382-1408.
-
(2006)
J. Multi. Anal.
, vol.97
, pp. 1382-1408
-
-
Baik, J.1
Silverstein, J.W.2
-
6
-
-
84855867843
-
On the largest eigenvalue of a Hermitian random matrix model with spiked external source I
-
preprint
-
J. Baik and D. Wang, On the largest eigenvalue of a Hermitian random matrix model with spiked external source I. Rank one case, preprint (2010); http://arxiv.org/1010.4604.
-
(2010)
Rank One Case
-
-
Baik, J.1
Wang, D.2
-
7
-
-
84855880530
-
On the largest eigenvalue of a Hermitian random matrix model with spiked external source II
-
preprint
-
J. Baik and D. Wang, On the largest eigenvalue of a Hermitian random matrix model with spiked external source II. Higher rank case, preprint (2011); http://arxiv.org//1104.2915.
-
(2011)
Higher Rank Case
-
-
Baik, J.1
Wang, D.2
-
8
-
-
84919673367
-
Wigner matrices
-
eds. G. Akemann, J. Baik and P. Di Francesco (Oxford University Press, New York
-
G. Ben Arous and A. Guionnet, Wigner matrices, in Oxford Handbook on Random Matrix Theory, eds. G. Akemann, J. Baik and P. Di Francesco (Oxford University Press, New York, 2011).
-
(2011)
Oxford Handbook on Random Matrix Theory
-
-
Ben Arous, G.1
Guionnet, A.2
-
9
-
-
80053163500
-
Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
-
F. Benaych-Georges, A. Guionnet and M. Maida, Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Electron. J. Probab. 16 (2011) 1621-1662.
-
(2011)
Electron. J. Probab.
, vol.16
, pp. 1621-1662
-
-
Benaych-Georges, F.1
Guionnet, A.2
Maida, M.3
-
10
-
-
84870540474
-
Large deviations of the extreme eigenvalues of random deformations of matrices
-
F. Benaych-Georges, A. Guionnet and M. Maida, Large deviations of the extreme eigenvalues of random deformations of matrices, Probab. Theory Related Fields 154(3-4) (2012) 703-751.
-
(2012)
Probab. Theory Related Fields
, vol.154
, Issue.3-4
, pp. 703-751
-
-
Benaych-Georges, F.1
Guionnet, A.2
Maida, M.3
-
11
-
-
79952708259
-
The eigenvalues and eigenvectors of finite low rank perturbations of large random matrices
-
F. Benaych-Georges and R. Rao, The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices, Adv. Math. 227(1) (2011) 494-521.
-
(2011)
Adv Math.
, vol.227
, Issue.1
, pp. 494-521
-
-
Benaych-Georges, F.1
Rao, R.2
-
15
-
-
63049133332
-
The largest eigenvalue of finite rank deformation of large Wigner matrices: Convergence and non universality of the fluctuations
-
M. Capitaine, C. Donati-Martin and D. Féral, The largest eigenvalue of finite rank deformation of large Wigner matrices: Convergence and non universality of the fluctuations, Ann. Probab. 37 (2009) 1-47.
-
(2009)
Ann. Probab.
, vol.37
, pp. 1-47
-
-
Capitaine, M.1
Donati-Martin, C.2
Féral, D.3
-
16
-
-
84856279561
-
Central limit theorems for eigenvalues of deformations of Wigner matrices
-
M. Capitaine, C. Donati-Martin and D. Féral, Central limit theorems for eigenvalues of deformations of Wigner matrices, Ann. 48(1) (2012) 107-133.
-
(2012)
Ann.
, vol.48
, Issue.1
, pp. 107-133
-
-
Capitaine, M.1
Donati-Martin, C.2
Féral, D.3
-
17
-
-
80755159232
-
Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices
-
M. Capitaine, C. Donati-Martin, D. Féral and M. Février, Free convolution with a semi-circular distribution and eigenvalues of spiked deformations of Wigner matrices, Electron. J. Probab. 16(64) (2011) 1750-1792.
-
(2011)
Electron. J. Probab.
, vol.16
, Issue.64
, pp. 1750-1792
-
-
Capitaine, M.1
Donati-Martin, C.2
Féral, D.3
Février, M.4
-
18
-
-
0000787440
-
The functional calculus
-
E. B. Davies, The functional calculus, J. London Math. Soc. 52 (1995) 166-176.
-
(1995)
J. London Math. Soc.
, vol.52
, pp. 166-176
-
-
Davies, E.B.1
-
19
-
-
80054099942
-
Universality of Wigner random matrices: A survey of recent results
-
L. Erdös, Universality ofWigner random matrices: A survey of recent results, Uspekhi Mat. Nauk 66 (2011) 67-198.
-
(2011)
Uspekhi Mat. Nauk
, vol.66
, pp. 67-198
-
-
Erdös, L.1
-
21
-
-
34248227713
-
The largest eigenvalue of rank one deformation of large Wigner matrices
-
D. Féral and S. Péché, The largest eigenvalue of rank one deformation of large Wigner matrices, Comm. Math. Phys. 272(1) (2007) 185-228.
-
(2007)
Comm. Math. Phys.
, vol.272
, Issue.1
, pp. 185-228
-
-
Féral, D.1
Péché, S.2
-
22
-
-
51249182622
-
The eigenvalues of random symmetric matrices
-
Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices, Combinatorica 1 (1981) 233-241.
-
(1981)
Combinatorica
, vol.1
, pp. 233-241
-
-
Füredi, Z.1
Komlós, J.2
-
24
-
-
0000301201
-
Equation de Schrödinger avec champ magnetique et equation de Harper
-
eds. H. Holden and A. Jensen Springer, Berlin
-
B. Helffer and J. Sjöstrand, Equation de Schrödinger avec champ magnetique et equation de Harper, in Schrödinger Operators, Lecture Notes in Physics, Vol. 345 eds. H. Holden and A. Jensen (Springer, Berlin, 1989), pp. 118-197.
-
(1989)
Schrödinger Operators, Lecture Notes in Physics
, vol.345
, pp. 118-197
-
-
Helffer, B.1
Sjöstrand, J.2
-
25
-
-
84856276225
-
Universality for certain Hermitian Wigner matrices under weak moment conditions
-
K. Johansson, Universality for certain Hermitian Wigner matrices under weak moment conditions, Ann. Inst. H. Doincaré Probab. Statist. 48(1) (2012) 47-79.
-
(2012)
Ann. Inst. H. Doincaré Probab. Statist.
, vol.48
, Issue.1
, pp. 47-79
-
-
Johansson, K.1
-
26
-
-
0035641726
-
On the distribution of the largest eigenvalue in principal components analysis
-
I. M. Johnstone, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29 (2001) 295-327.
-
(2001)
Ann. Statist.
, vol.29
, pp. 295-327
-
-
Johnstone, I.M.1
-
27
-
-
0030494613
-
Asymptotic properties of large random matrices with independent entries
-
A. Khorunzhy, B. Khoruzhenko and L. Pastur, Asymptotic properties of large random matrices with independent entries, J. Math. Phys. 37 (1996) 5033-5060.
-
(1996)
J. Math. Phys.
, vol.37
, pp. 5033-5060
-
-
Khorunzhy, A.1
Khoruzhenko, B.2
Pastur, L.3
-
32
-
-
58549092109
-
Fluctuations of matrix elements of regular functions of Gaussian random matrices
-
A. Lytova and L. Pastur, Fluctuations of matrix elements of regular functions of Gaussian random matrices, J. Statist. Phys. 134 (2009) 147-159.
-
(2009)
J. Statist. Phys.
, vol.134
, pp. 147-159
-
-
Lytova, A.1
Pastur, L.2
-
34
-
-
34548315757
-
Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles
-
M. Maida, Large deviations for the largest eigenvalue of rank one deformations of Gaussian ensembles, Electron. J. Probab. 12 (2007) 1131-1150.
-
(2007)
Electron. J. Probab.
, vol.12
, pp. 1131-1150
-
-
Maida, M.1
-
36
-
-
84879219252
-
On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries
-
to appear
-
S. O'Rourke, D. Renfrew and A. Soshnikov, On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, to appear in J. Theoret. Probab.
-
J. Theoret. Probab
-
-
O'Rourke, S.1
Renfrew, D.2
Soshnikov, A.3
-
37
-
-
38549175880
-
Asymptotics of sample eigenstructure for a large dimensional spiked covariance model
-
D. Paul, Asymptotics of sample eigenstructure for a large dimensional spiked covariance model, Statist. Sinica 17(4) (2007) 1617-1642.
-
(2007)
Statist. Sinica
, vol.17
, Issue.4
, pp. 1617-1642
-
-
Paul, D.1
-
38
-
-
28144463102
-
The largest eigenvalue of small rank perturbations of Hermitian random matrices
-
S. Péché, The largest eigenvalue of small rank perturbations of Hermitian random matrices, Probab. Theory Related Fields 134(1) (2006) 127-173.
-
(2006)
Probab. Theory Related Fields
, vol.134
, Issue.1
, pp. 127-173
-
-
Péché, S.1
-
40
-
-
84855885363
-
Fluctuations of matrix entries of regular functions of Wigner matrices
-
A. Pizzo, D. Renfrew and A. Soshnikov, Fluctuations of matrix entries of regular functions of Wigner matrices, J. Statist. Phys. 146(3) (2012) 550-591.
-
(2012)
J. Statist. Phys.
, vol.146
, Issue.3
, pp. 550-591
-
-
Pizzo, A.1
Renfrew, D.2
Soshnikov, A.3
-
41
-
-
84860437102
-
Central limit theorem for linear eigenvalue statistics of Wigner and sample covariance random matrices
-
M. Shcherbina, Central limit theorem for linear eigenvalue statistics of Wigner and sample covariance random matrices, J. Math. Phys. Anal. Geome. 7(2) (2011) 176-192.
-
(2011)
J. Math. Phys. Anal. Geome.
, vol.7
, Issue.2
, pp. 176-192
-
-
Shcherbina, M.1
-
43
-
-
85081395630
-
Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs
-
preprint
-
M. Shcherbina and B. Tirozzi, Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs. Diluted regime, preprint (2011); arXiv.1111.5492.
-
(2011)
Diluted Regime
-
-
Shcherbina, M.1
Tirozzi, B.2
-
44
-
-
0033473406
-
Universality at the edge of the spectrum in Wigner random matrices
-
A. Soshnikov, Universality at the edge of the spectrum in Wigner random matrices, Commun. Math. Phys. 207 (1999) 697-733.
-
(1999)
Commun. Math. Phys.
, vol.207
, pp. 697-733
-
-
Soshnikov, A.1
-
45
-
-
84941460976
-
Bedingt konvergente Reihen und konvexe Systeme
-
E. Steinitz, Bedingt konvergente Reihen und konvexe Systeme, J. Reine Angew. Math. 143 (1913) 128-175.
-
(1913)
J. Reine Angew. Math.
, vol.143
, pp. 128-175
-
-
Steinitz, E.1
-
46
-
-
84872653524
-
Outliers in the spectrum of iid matrices with bounded rank perturbations
-
T. Tao, Outliers in the spectrum of iid matrices with bounded rank perturbations, Probab. Theory Related Fields. 155(1-2) (2013) 231-263.
-
(2013)
Probab. Theory Related Fields.
, vol.155
, Issue.1-2
, pp. 231-263
-
-
Tao, T.1
-
47
-
-
77954624704
-
Random matrices: Universality of local eigenvalue statistics up to the edge
-
T. Tao and V. Vu, Random matrices: Universality of local eigenvalue statistics up to the edge, Commun. Math. Phys. 298 (2010) 549-572.
-
(2010)
Commun. Math. Phys.
, vol.298
, pp. 549-572
-
-
Tao, T.1
Vu, V.2
-
49
-
-
27644532196
-
Level spacing distributions and the Airy kernel
-
C. Tracy and H. Widom, Level spacing distributions and the Airy kernel, Commun. Math. Phys. 159 (1994) 151-174.
-
(1994)
Commun. Math. Phys.
, vol.159
, pp. 151-174
-
-
Tracy, C.1
Widom, H.2
-
50
-
-
0030545965
-
On orthogonal and symplectic matrix ensembles
-
C. Tracy and H. Widom, On orthogonal and symplectic matrix ensembles, Commun. Math. Phys. 177 (1996) 727-754.
-
(1996)
Commun. Math. Phys.
, vol.177
, pp. 727-754
-
-
Tracy, C.1
Widom, H.2
|