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Some estimates of norms of random matrices
Author(s):
Rafal
Latala
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1273-1282.
MSC (2000):
Primary 15A52;
Secondary 60G15
Posted:
December 15, 2004
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Abstract |
References |
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Additional information
Abstract:
We show that for any random matrix  with independent mean zero entries
where  is some universal constant.
References:
- 1.
- S. Chevet, Séries de variables aléatoires gaussiennes à valeurs dans
 . Application aux produits Wiener abstraits, Séminaire sur la Géométrie des Espaces de Banach (1977-1978), Exp No. 19, École Polytechnique, Palaiseau, 1978. MR 0520217 (81g:60004) - 2.
- S. Geman, A limit theorem for the norm of random matrices, Ann. Probab. 8 (1980), 252-261. MR 0566592 (81m:60046)
- 3.
- M. Ledoux, The concentration of measure phenomenon, American Mathematical Society, Providence, RI, 2001. MR 1849347 (2003k:28019)
- 4.
- Y. Seginer, The expected norm of random matrices, Combin. Probab. Comput. 9 (2000), 149-166. MR 1762786 (2001a:62070)
- 5.
- J.W. Silverstein, ,J. Multivariate Anal. 30 (1989), 307-311. MR 1015375 (90m:62121)
- 6.
- S. Szarek, Condition numbers of random matrices, J. Complexity 7 (1991), 131-149. MR 1108773 (92i:65086)
- 7.
- E. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. of Math. 62 (1955), 548-564. MR 0077805 (17:1097c)
- 8.
- Y.Q. Yin, Z.D. Bai and P.R. Krishnaiah, On the limit of the largest eigenvalue of the large sample covariance matrix, Probab. Theory Relat. Fields 78 (1988), 509-521. MR 0950344 (89g:60117)
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Additional Information:
Rafal
Latala
Affiliation:
Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Email:
rlatala@mimuw.edu.pl
DOI:
10.1090/S0002-9939-04-07800-1
PII:
S 0002-9939(04)07800-1
Keywords:
Random matrices,
operator norm
Received by editor(s):
June 27, 2002
Received by editor(s) in revised form:
October 15, 2003
Posted:
December 15, 2004
Additional Notes:
This research was partially supported by KBN grant \#2 PO3A 027 22
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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![\begin{displaymath}\mathbf{E}\Vert(X_{ij})\Vert\leq C \Big(\max_{i}\sqrt{\sum_{j... ...} X_{ij}^{2}}+ \sqrt[4]{\sum_{ij} \mathbf{E} X_{ij}^{4}} \Big),\end{displaymath}](/proc/2005-133-05/S0002-9939-04-07800-1/gif-abstract0/img2.gif)
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