| On random pm 1 matrices: singularity and determinant |
| Full text |
Pdf
(242 KB)
|
| Source
|
Annual ACM Symposium on Theory of Computing
archive
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
table of contents
Baltimore, MD, USA
SESSION: Session 9B
table of contents
Pages: 431 - 440
Year of Publication: 2005
ISBN:1-58113-960-8
|
|
Authors
|
|
| Sponsors |
|
| Publisher |
|
| Bibliometrics |
Downloads (6 Weeks): 13, Downloads (12 Months): 54, Citation Count: 1
|
|
|
ABSTRACT
We proved several results concerning the determinant of a random pm 1 matrix. In particular, we show that with high probability, the determinant has absolute value very close to √n!.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
| |
1
|
Z. Bai and Y. Yin, Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix, Ann. Probab. 21 (1993), no. 3, 1275--1294.
|
| |
2
|
J. Bourgain, personal communication.
|
| |
3
|
P. Erdös, On a lemma of Littlewood and Offord, Bull. Amer. Math. Soc. 51 (1945), 898--902.
|
| |
4
|
C.G. Esséen, On the Kolmogorov-Rogozin inequality for the concentration function, Z. Wahrsch. Verw. Gebiete 5 (1966), 210--216.
|
| |
5
|
G. Halasz, On the distribution of additive arithmetic functions, Acta Arith. 27 (1975), 143--152.
|
| |
6
|
J. Kahn, J. Komlós, E. Szemerédi, On the probability that a random pm 1 matrix is singular, J. Amer. Math. Soc. 8 (1995), 223--240.
|
| |
7
|
J. Komlós, On the determinant of (0,1) matrices, Studia Sci. Math. Hungar. 2 (1967) 7--22.
|
| |
8
|
J. Komlós, On the determinant of random matrices, Studia Sci. Math. Hungar. 3 (1968) 387--399.
|
| |
9
|
A.M. Macbeath, On measure of sum sets II. The sum-theorem for the torus, Proc. Cambridge Phil. Soc. 49 (1953), 40--43.
|
| |
10
|
|
| |
11
|
P. Turán, On extremal problems concerning determinants, (Hungarian) Math. Naturwiss. Anz. Ungar. Akad. Wiss. 59, (1940). 95--105
|
|