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Let $M_n$ be a random matrix of size $n\times n$ and let $\lambda_1,...,\lambda_n$ be the eigenvalues of $M_n$.
J. E. Littlewood and A. C. Offord, On the number of real roots of a random algebraic equation . III. Rec. Math. Mat. Sbornik N.S. 12 , (1943). 277–286
1943
Earlier work this paper cites.
P. Erdős, On a lemma of Littlewood and Offord , Bull. Amer. Math. Soc. 51 (1945), 898-902
1945
Earlier work this paper cites.
P. Erdős and L. Moser, Elementary Problems and Solutions : Solutions: E736. Amer. Math. Monthly, 54 (1947), no. 4, 229-230
1947
Earlier work this paper cites.
A. Sárközy and E. Szemerédi, Über ein Problem von Erdős und Moser , Acta Arithmetica 11 (1965), 205-208
1965
Earlier work this paper cites.
C. G. Esséen, On the Kolmogorov-Rogozin inequality for the concentration function , Z. Wahrsch. Verw. Gebiete 5 (1966), 210-216
1966
Earlier work this paper cites.
G. Katona, On a conjecture of Erdős and a stronger form of Sperner’s theorem . Studia Sci. Math. Hungar 1 (1966), 59-63
1966
Earlier work this paper cites.
D. Kleitman, On a lemma of Littlewood and Offord on the distributions of linear combinations of vectors , Advances in Math. 5 (1970), 155-157
1970
Earlier work this paper cites.
G. Halász, Estimates for the concentration function of combinatorial number theory and probability , Period. Math. Hungar. 8 (1977), no. 3-4, 197-211
1977
Earlier work this paper cites.
V. L. Girko, Circular law
1984
Earlier work this paper cites.
J. Kahn, J. Komlós and E. Szemerédi, On the probability that a random ± 1 \pm 1 matrix is singular , J. Amer. Math. Soc. 8 (1995), 223-240
1995
Earlier work this paper cites.
M. Talagrand, A new look at independence , Ann. Probab. 24 (1996), no. 1, 1-34
1996
Cited alongside, same era.
Z. D. Bai, Circular law
1997
Cited alongside, same era.
V. L. Girko, The strong circular law, Twenty years later
2004
Cited alongside, same era.
Z. D. Bai and J. Silverstein, Spectral analysis of large dimensional random matrices
2006
Cited alongside, same era.
K. Costello, T. Tao and V. Vu, Random symmetric matrices are almost surely non-singular , Duke Math. J. 135 (2006), 395-413
2006
Cited alongside, same era.
T. Tao and V. Vu, On random ± 1 \pm 1 matrices: singularity and determinant
2006
Cited alongside, same era.
T. Tao and V. Vu, Inverse Littlewood-Offord theorems and the condition number of random matrices , Annals of Mathematics (2) 169 (2009), no 2, 595-632
2009
Later among the works it cites.
T. Tao and V. Vu, From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices,
2009
Later among the works it cites.
D. Chafai, The Dirichlet Markov Ensemble
2010
Later among the works it cites.
F. Götze and A. N. Tikhomirov, The circular law for random matrices
2010
Later among the works it cites.
G. Pan and W. Zhou, Circular law, extreme singular values and potential theory
2010
Later among the works it cites.
T. Tao and V. Vu, A sharp inverse Littlewood-Offord theorem , Random Structures and Algorithms, Vol. 37 4 (2010), 525-539
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T. Tao and V. Vu, On the singularity probability of random Bernoulli matrices , J. Amer. Math. Soc. 20 (2007), 603-628
2007
Cited alongside, same era.
M. Rudelson and R. Vershynin, The Littlewood-Offord Problem and invertibility of random matrices , Advances in Mathematics 218 (2008), 600-633
2008
Cited alongside, same era.
T. Tao and V. Vu, Random matrices: the circular law , Communications in Contemporary Mathematics, 10 (2008), 261-307
2008
Cited alongside, same era.
C. Bordenave, P. Caputo, D. Chafai, Circular law theorem for random Markov matrices
Cited in the paper.
H. Nguyen, Inverse Littlewood-Offord problems and the singularity of random symmetric matrices , to appear in Duke Math. J
Cited in the paper.
H. Nguyen, Random doubly stochastic matrices: the circular law , in preparation
Cited in the paper.
2010
Later among the works it cites.
T. Tao and V. Vu, Smooth analysis of the condition number and the least singular value
2010
Later among the works it cites.
H. Nguyen and V. Vu, Optimal Littlewood-Offord theorems , Advances in Mathematics, Vol. 226 6 (2011), 5298-5319
2011
Later among the works it cites.
T. Tao, V. Vu and appendix by M. Krishnapur, Random matrices: universality of ESDs and the circular law , Annals of Probability 38 (2010), no. 5, 2023-2065
2065
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