-
1
-
-
49649124324
-
Smallest singular value of random matrices with independent columns
-
Adamczak R., Guédon O., Litvak A., Pajor A., Tomczak-Jaegermann N.: Smallest singular value of random matrices with independent columns. C. R. Math. Acad. Sci. Paris 346(15-16), 853-856 (2008).
-
(2008)
C. R. Math. Acad. Sci. Paris
, vol.346
, Issue.15-16
, pp. 853-856
-
-
Adamczak, R.1
Guédon, O.2
Litvak, A.3
Pajor, A.4
Tomczak-Jaegermann, N.5
-
2
-
-
36448938113
-
Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem
-
Akemann G., Kanzieper E.: Integrable structure of Ginibre's ensemble of real random matrices and a Pfaffian integration theorem. J. Stat. Phys. 129(5-6), 1159-1231 (2007).
-
(2007)
J. Stat. Phys.
, vol.129
, Issue.5-6
, pp. 1159-1231
-
-
Akemann, G.1
Kanzieper, E.2
-
3
-
-
33750047519
-
n
-
n.Positivity 10(4), 755-759 (2006).
-
(2006)
Positivity
, vol.10
, Issue.4
, pp. 755-759
-
-
Aubrun, G.1
-
4
-
-
0031534271
-
Circular law
-
Bai Z. D.: Circular law. Ann. Probab. 25(1), 494-529 (1997).
-
(1997)
Ann. Probab.
, vol.25
, Issue.1
, pp. 494-529
-
-
Bai, Z.D.1
-
6
-
-
38249027279
-
A note on the largest eigenvalue of a large-dimensional sample covariance matrix
-
Bai Z. D., Silverstein J. W., Yin Y. Q.: A note on the largest eigenvalue of a large-dimensional sample covariance matrix. J. Multivar. Anal. 26(2), 166-168 (1988).
-
(1988)
J. Multivar. Anal.
, vol.26
, Issue.2
, pp. 166-168
-
-
Bai, Z.D.1
Silverstein, J.W.2
Yin, Y.Q.3
-
7
-
-
0010883127
-
Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang
-
Bai Z. D., Yin Y. Q.: Limiting behavior of the norm of products of random matrices and two problems of Geman-Hwang. Probab. Theory Relat. Fields 73(4), 555-569 (1986).
-
(1986)
Probab. Theory Relat. Fields
, vol.73
, Issue.4
, pp. 555-569
-
-
Bai, Z.D.1
Yin, Y.Q.2
-
8
-
-
0001758959
-
Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix
-
Bai Z. D., Yin Y. Q.: Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix. Ann. Probab. 21(3), 1275-1294 (1993).
-
(1993)
Ann. Probab.
, vol.21
, Issue.3
, pp. 1275-1294
-
-
Bai, Z.D.1
Yin, Y.Q.2
-
9
-
-
1042275757
-
Computation of some examples of Brown's spectral measure in free probability
-
Biane Ph., Lehner F.: Computation of some examples of Brown's spectral measure in free probability. Colloq. Math. 90(2), 181-211 (2001).
-
(2001)
Colloq. Math.
, vol.90
, Issue.2
, pp. 181-211
-
-
Biane, P.1
Lehner, F.2
-
10
-
-
1642373920
-
Random graphs
-
2nd edn. Cambridge University Press, Cambridge
-
Bollobás, B.: Random graphs. Cambridge Studies in Advanced Mathematics, vol. 73, 2nd edn. Cambridge University Press, Cambridge (2001).
-
(2001)
Cambridge Studies in Advanced Mathematics
, vol.73
-
-
Bollobás, B.1
-
11
-
-
84858149146
-
Spectrum of large random reversible Markov chains: Heavy-tailed weigths on the complete graph
-
Preprint (accepted). arXiv: 0903. 3528 [math. PR]
-
Bordenave, Ch., Caputo, P., Chafaï, D.: Spectrum of large random reversible Markov chains: Heavy-tailed weigths on the complete graph. Ann. Probab. (2010). Preprint (accepted). arXiv: 0903. 3528 [math. PR].
-
(2010)
Ann. Probab
-
-
Bordenave, C.1
Caputo, P.2
Chafaï,, D.3
-
12
-
-
80051642686
-
Spectrum of large random reversible markov chains: two examples
-
Bordenave, Ch., Caputo, P., Chafaï, D.: Spectrum of large random reversible markov chains: two examples. ALEA Latin Am. J. Probab. Math. Stat. (7), 41-64 (2010).
-
(2010)
ALEA Latin Am. J. Probab. Math. Stat
, Issue.7
, pp. 41-64
-
-
Bordenave, C.1
Caputo, P.2
Chafaï,, D.3
-
13
-
-
80051626082
-
-
(preprint)
-
Bordenave, Ch., Caputo, P., Chafaï, D.: Spectrum of non-Hermitian heavy tailed random matrices (2010, preprint).
-
(2010)
Spectrum of non-Hermitian heavy tailed random matrices
-
-
Bordenave, C.1
Caputo, P.2
Chafaï,, D.3
-
14
-
-
0002792520
-
Lidskiǐ's theorem in the type II case. Geometric Methods in Operator Algebras
-
(Kyoto, 1983), Longman Sci. Tech. Harlow
-
Brown, L. G.: Lidskiǐ's theorem in the type II case. Geometric Methods in Operator Algebras (Kyoto, 1983). Pitman Res. Notes Math. Ser., vol. 123, pp. 1-35. Longman Sci. Tech. Harlow (1986).
-
(1986)
Pitman Res. Notes Math. Ser
, vol.123
, pp. 1-35
-
-
Brown, L.G.1
-
15
-
-
70450193509
-
Aspects of large random Markov kernels
-
Chafaï D.: Aspects of large random Markov kernels. Stochastics 81(3-4), 415-429 (2009).
-
(2009)
Stochastics
, vol.81
, Issue.3-4
, pp. 415-429
-
-
Chafaï, D.1
-
16
-
-
78149501031
-
Circular law for noncentral random matrices
-
Chafaï D.: Circular law for noncentral random matrices. J. Theor. Probab. 23(4), 945-950 (2010).
-
(2010)
J. Theor. Probab.
, vol.23
, Issue.4
, pp. 945-950
-
-
Chafaï, D.1
-
17
-
-
72549087149
-
The Dirichlet Markov ensemble
-
Chafaï D.: The Dirichlet Markov ensemble. J. Multivar. Anal. 101, 555-567 (2010).
-
(2010)
J. Multivar. Anal.
, vol.101
, pp. 555-567
-
-
Chafaï, D.1
-
18
-
-
33846999295
-
On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices
-
Dozier R. B., Silverstein J. W.: On the empirical distribution of eigenvalues of large dimensional information-plus-noise-type matrices. J. Multivar. Anal. 98(4), 678-694 (2007).
-
(2007)
J. Multivar. Anal.
, vol.98
, Issue.4
, pp. 678-694
-
-
Dozier, R.B.1
Silverstein, J.W.2
-
19
-
-
0031068715
-
The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law
-
Edelman A.: The probability that a random real Gaussian matrix has k real eigenvalues, related distributions, and the circular law. J. Multivar. Anal. 60(2), 203-232 (1997).
-
(1997)
J. Multivar. Anal.
, vol.60
, Issue.2
, pp. 203-232
-
-
Edelman, A.1
-
23
-
-
33845679351
-
Strong circular law
-
Girko V. L.: Strong circular law. Random Oper. Stoch. Equ. 5(2), 173-196 (1997).
-
(1997)
Random Oper. Stoch. Equ.
, vol.5
, Issue.2
, pp. 173-196
-
-
Girko, V.L.1
-
24
-
-
33845661409
-
The circular law. Twenty years later. III
-
Girko V. L.: The circular law. Twenty years later. III. Random Oper. Stoch. Equ. 13(1), 53-109 (2005).
-
(2005)
Random Oper. Stoch. Equ.
, vol.13
, Issue.1
, pp. 53-109
-
-
Girko, V.L.1
-
25
-
-
0041914118
-
Distribution of subdominant eigenvalues of matrices with random rows
-
electronic
-
Goldberg G., Neumann M.: Distribution of subdominant eigenvalues of matrices with random rows. SIAM J. Matrix Anal. Appl. 24(3), 747-761 (2003) electronic.
-
(2003)
SIAM J. Matrix Anal. Appl.
, vol.24
, Issue.3
, pp. 747-761
-
-
Goldberg, G.1
Neumann, M.2
-
26
-
-
77957039680
-
The circular law for random matrices
-
Götze F., Tikhomirov A.: The circular law for random matrices. Ann. Probab. 38(4), 1444-1491 (2010).
-
(2010)
Ann. Probab.
, vol.38
, Issue.4
, pp. 1444-1491
-
-
Götze, F.1
Tikhomirov, A.2
-
27
-
-
33746374167
-
On the eigenvalues of a matrix with prescribed singular values
-
Horn A.: On the eigenvalues of a matrix with prescribed singular values. Proc. Am. Math. Soc. 5, 4-7 (1954).
-
(1954)
Proc. Am. Math. Soc.
, vol.5
, pp. 4-7
-
-
Horn, A.1
-
28
-
-
0003952516
-
-
Cambridge University Press, Cambridge (Corrected reprint of the 1991 original)
-
Horn, R. A., Johnson, Ch. R.: Topics in matrix analysis. Cambridge University Press, Cambridge (1994, Corrected reprint of the 1991 original).
-
(1994)
Topics in matrix analysis
-
-
Horn, R.A.1
Johnson, C.R.2
-
29
-
-
0010884799
-
A brief survey on the spectral radius and the spectral distribution of large random matrices with i. i. d. entries. Random Matrices and their Applications
-
(Brunswick, Maine, 1984), American Mathematical Society, Providence, RI
-
Hwang, C.-R.: A brief survey on the spectral radius and the spectral distribution of large random matrices with i. i. d. entries. Random Matrices and their Applications (Brunswick, Maine, 1984). Contemp. Math, vol. 50. American Mathematical Society, Providence, RI, pp. 145-152 (1986).
-
(1986)
Contemp. Math
, vol.50
, pp. 145-152
-
-
Hwang, C.-R.1
-
30
-
-
0012942540
-
The concentration of measure phenomenon
-
American Mathematical Society, Providence, RI
-
Ledoux, M.: The concentration of measure phenomenon. Mathematical Surveys and Monographs, vol. 89. American Mathematical Society, Providence, RI (2001).
-
(2001)
Mathematical Surveys and Monographs
, vol.89
-
-
Ledoux, M.1
-
31
-
-
0000263239
-
The distribution of eigenvalues in sertain sets of random matrices
-
Marchenko V. A., Pastur L. A: The distribution of eigenvalues in sertain sets of random matrices. Mat. Sb. 72, 507-536 (1967).
-
(1967)
Mat. Sb.
, vol.72
, pp. 507-536
-
-
Marchenko, V.A.1
Pastur, L.A.2
-
33
-
-
72549096261
-
Circular law, extreme singular values and potential theory
-
Pan G. M., Zhou W.: Circular law, extreme singular values and potential theory. J. Multivar. Anal 101(3), 645-656 (2010).
-
(2010)
J. Multivar. Anal
, vol.101
, Issue.3
, pp. 645-656
-
-
Pan, G.M.1
Zhou, W.2
-
34
-
-
41049114969
-
The Littlewood-Offord problem and invertibility of random matrices
-
Rudelson M., Vershynin R.: The Littlewood-Offord problem and invertibility of random matrices. Adv. Math. 218(2), 600-633 (2008).
-
(2008)
Adv. Math.
, vol.218
, Issue.2
, pp. 600-633
-
-
Rudelson, M.1
Vershynin, R.2
-
35
-
-
0003869516
-
-
Springer, Berlin (Appendix B by Thomas Bloom)
-
Saff, E. B., Totik, V.: Logarithmic potentials with external fields, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 316. Springer, Berlin (1997, Appendix B by Thomas Bloom).
-
(1997)
Logarithmic potentials with external fields, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
, vol.316
-
-
Saff, E.B.1
Totik, V.2
-
37
-
-
33847058040
-
The spectral radii and norms of large-dimensional non-central random matrices
-
Silverstein J. W.: The spectral radii and norms of large-dimensional non-central random matrices. Commun. Stat. Stoch. Models 10(3), 525-532 (1994).
-
(1994)
Commun. Stat. Stoch. Models
, vol.10
, Issue.3
, pp. 525-532
-
-
Silverstein, J.W.1
-
38
-
-
0037143983
-
Random regularization of Brown spectral measure
-
Śniady P.: Random regularization of Brown spectral measure. J. Funct. Anal 193(2), 291-313 (2002).
-
(2002)
J. Funct. Anal
, vol.193
, Issue.2
, pp. 291-313
-
-
Śniady, P.1
-
39
-
-
51249165477
-
Concentration of measure and isoperimetric inequalities in product spaces
-
Talagrand, M.: Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Études Sci. Publ. Math (81) 73-205 (1995).
-
(1995)
Inst. Hautes Études Sci. Publ. Math
, Issue.81
, pp. 73-205
-
-
Talagrand, M.1
-
40
-
-
44249125025
-
Random matrices: the circular law
-
Tao T., Vu V.: Random matrices: the circular law. Commun. Contemp. Math. 10(2), 261-307 (2008).
-
(2008)
Commun. Contemp. Math.
, vol.10
, Issue.2
, pp. 261-307
-
-
Tao, T.1
Vu, V.2
-
41
-
-
77957124985
-
Random matrices: universality of ESDs and the circular law
-
(With an appendix by Manjunath Krishnapur)
-
Tao, T., Vu, V.: Random matrices: universality of ESDs and the circular law. Ann. Probab. 38(5), 2023-2065 (2010, With an appendix by Manjunath Krishnapur).
-
(2010)
Ann. Probab.
, vol.38
, Issue.5
, pp. 2023-2065
-
-
Tao, T.1
Vu, V.2
-
42
-
-
0016896723
-
The behavior of eigenvalues and singular values under perturbations of restricted rank
-
(Collection of articles dedicated to Olga Taussky Todd)
-
Thompson, R. C.: The behavior of eigenvalues and singular values under perturbations of restricted rank. Linear Algebra Appl. 13 (1/2), 69-78 (1976. Collection of articles dedicated to Olga Taussky Todd).
-
(1976)
Linear Algebra Appl
, vol.13
, Issue.1-2
, pp. 69-78
-
-
Thompson, R.C.1
-
45
-
-
0002247902
-
The strong limits of random matrix spectra for sample matrices of independent elements
-
Wachter K. W.: The strong limits of random matrix spectra for sample matrices of independent elements. Ann. Probab. 6(1), 1-18 (1978).
-
(1978)
Ann. Probab.
, vol.6
, Issue.1
, pp. 1-18
-
-
Wachter, K.W.1
-
46
-
-
0000142609
-
Inequalities between the two kinds of eigenvalues of a linear transformation
-
Weyl H.: Inequalities between the two kinds of eigenvalues of a linear transformation. Proc. Nat. Acad. Sci. USA 35, 408-411 (1949).
-
(1949)
Proc. Nat. Acad. Sci. USA
, vol.35
, pp. 408-411
-
-
Weyl, H.1
-
47
-
-
0003059603
-
Limiting spectral distribution for a class of random matrices
-
Yin Y. Q.: Limiting spectral distribution for a class of random matrices. J. Multivar. Anal. 20(1), 50-68 (1986).
-
(1986)
J. Multivar. Anal.
, vol.20
, Issue.1
, pp. 50-68
-
-
Yin, Y.Q.1
|