On random ± 1 matrices: Singularity and determinant

Random Structures and Algorithms

Volumn 28, Issue 1, 2006, Pages 1-23

  Tao, Terence ^a   Vu, Van ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33645288547     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20109     Document Type: Article

References (15)

1. Z. Bai and Y. Yin, Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix, Ann Probabil 21 (1993), 1275-1294.
2. p (G), Ann Inst Fourier 20 (1970), 335-402.
3. P. Erdös, On a lemma of Littlewood and Offord, Bull Am 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. V. L. Girko, Theory of random determinants. Translated from the Russian. Mathematics and its Applications (Soviet Series), 45. Kluwer Academic, Dordrecht, 1990.
6. G. Halász, On the distribution of additive arithmetic functions, Acta Arith 27 (1975), 143-152.
7. J. Kahn, J. Komlós, E. Szemerédi, On the probability that a random ± 1 matrix is singular, J Am Math Soc 8 (1995), 223-240.
8. J. Komlós, On the determinant of (0, 1) matrices, Stud Sci Math Hungar 2 (1967), 7-22.
9. J. Komlós, On the determinant of random matrices, Stud Sci Math Hungar 3 (1968), 387-399.
10. A. M. Macbeath, On measure of sum sets II. The sum-theorem for the torus, Proc Cambridge Phil Soc 49 (1953), 40-43.
11. A. Odlyzko, On subspaces spanned by random selections of ±1 vectors, J Combin Theory A 47(1988), 124-133.
12. M. Talagrand, A new look at independence, Ann Probabil 24 (1996), 1-34.
13. T. Tao, V. Vu, On the singularity probability of random Bernoulli matrices, preprint (arXiv:math.CO/0501313).
14. P. Turán, On extremal problems concerning determinants, (Hungarian) Math Naturwiss Anz Ungar Akad Wiss 59 (1940), 95-105.
15. T. Voight, G. Ziegler, Singular 0/1 matrices and the hyperplanes spanned by random 0/1 vectors, preprint (arXiv:math.CO/0308050).