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Let $ A_n $ be an $n \times n$ random matrix with i.i.d Bernoulli($p$) entries.
The rank of sparse random matrices
A. Coja-Oghlan, A. Ergr, P. Gao, S. Hetterich, and M. Rolvien · 1906
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The smallest singular value of inhomogeneous square random matrices
G. Livshyts, K. Tikhomirov, and R. Vershynin · 1909
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On the determinant of ( 0 , 1 ) (0,1) matrices
J. Komlós · 1967
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On the probability that a random ± 1 \pm 1 matrix is singular
J. Kahn, J. Komlós, and E. Szemerédi · 1995
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Singularity of sparse Bernoulli mattrices
K. Tikhomirov and A. Litvak · 2004
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Recent Progress In Combinatorial Random Matrix Theory
V. Vu · 2005
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On random ± 1 \pm 1 matrices: singularity and determinant
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On the singularity probability of random Bernoulli matrices
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The Rank of Random graphs
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E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef · 2016
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Adjacency matrices of random digraphs: singularity and anti-concentration
E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef · 2017
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The rank of random regular digraphs of constant degree
E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef · 2018
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Structure of eigenvectors of random regular digraphs
E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef · 2019
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The smallest singular value of a shiftedd-regular random square matrix
E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef · 2019
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On the Rank of Random Sparse Matrices
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V. Jain, A. Sah, and M. Sawhney · 2010
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Sharp transition of the invertibility of the adjacency matrices of random graphs
A. Basak and M Rudelson
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Rank deficiency of random matrices
V. Jain, A. Sah, and M. Sawhney
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The circular law for sparse random regular digraphs
E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef
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The smallest singular value of heavy-tailed not necessary i.i.d random matrices via random rounding
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Covering of random ellipsoids, and invertibility of random matrices with i.i.d heavy-tailed entries
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K. Costello and V. Vu · 2020
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