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Let $A$ be the adjacency matrix of a uniformly random $d$-regular digraph on $n$ vertices, and suppose that $\min(d,n-d)\geq\lambda n$.
1904
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1904
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1904
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1909
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2017
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Alexander E. Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef, Adjacency matrices of random digraphs: singularity and anti-concentration , J. Math. Anal. Appl. 445
2017
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Alexander E. Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef, Adjacency matrices of random digraphs: singularity and anti-concentration , J. Math. Anal. Appl. 445
2017
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Hoi H. Nguyen, On the singularity of random combinatorial matrices , SIAM J. Discrete Math. 27
2013
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Hoi H. Nguyen and Van H. Vu, Circular law for random discrete matrices of given row sum , J. Comb. 4
2013
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Roman Vershynin, Invertibility of symmetric random matrices , Random Structures Algorithms 44
2014
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Mark Rudelson and Roman Vershynin, No-gaps delocalization for general random matrices , Geom. Funct. Anal. 26
2016
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Nicholas A. Cook, On the singularity of adjacency matrices for random regular digraphs , Probab. Theory Related Fields 167
2017
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Cited in the paper.
Cited in the paper.
Nicholas Cook, The circular law for random regular digraphs , Ann. Inst. Henri Poincaré Probab. Stat. 55
2019
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Asaf Ferber and Vishesh Jain, Singularity of random symmetric matrices—a combinatorial approach to improved bounds , Forum Math. Sigma 7
2019
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2019
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Alexander E. Litvak, Anna Lytova, Konstantin Tikhomirov, Nicole Tomczak-Jaegermann, and Pierre Youssef, The smallest singular value of a shifted d d -regular random square matrix , Probab. Theory Related Fields 173
2019
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Konstantin Tikhomirov, Singularity of random Bernoulli matrices , Ann. of Math. (2) 191
2020
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Terence Tao and Van Vu, Random matrices: universality of ESDs and the circular law , Ann. Probab. 38
2065
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