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Comptes Rendus. Mathématique
Probabilités
Singularity of random symmetric matrices – simple proof
Comptes Rendus. Mathématique, Tome 359 (2021) no. 6, pp. 743-747.

In this paper we give a simple, short, and self-contained proof for a non-trivial upper bound on the probability that a random ±1 symmetric matrix is singular.

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DOI : https://doi.org/10.5802/crmath.215
Asaf Ferber 1

1. Department of Mathematics, University of California, Irvine, USA.
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     title = {Singularity of random symmetric matrices {\textendash} simple proof},
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Asaf Ferber. Singularity of random symmetric matrices – simple proof. Comptes Rendus. Mathématique, Tome 359 (2021) no. 6, pp. 743-747. doi : 10.5802/crmath.215. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.215/

[1] Marcelo Campos; Letícia Mattos; Robert Morris; Natasha Morrison On the singularity of random symmetric matrices (2019) (https://arxiv.org/abs/1904.11478) | Zbl 1467.60005

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[3] Asaf Ferber; Vishesh Jain Singularity of random symmetric matrices—a combinatorial approach to improved bounds, Forum Math. Sigma, Volume 7 (2019), e22 | MR 3993806 | Zbl 1423.60016

[4] Asaf Ferber; Vishesh Jain; Kyle Luh; Wojciech Samotij On the counting problem in inverse Littlewood–Offord theory (2019) (https://arxiv.org/abs/1904.10425) | Zbl 07381839

[5] Jiaoyang Huang Invertibility of adjacency matrices for random d-regular graphs (2018) (https://arxiv.org/abs/1807.06465)

[6] Hoi H Nguyen Inverse Littlewood–Offord problems and the singularity of random symmetric matrices, Duke Math. J., Volume 161 (2012) no. 4, pp. 545-586 | MR 2891529 | Zbl 1276.15019

[7] Roman Vershynin Invertibility of symmetric random matrices, Random Struct. Algorithms, Volume 44 (2014) no. 2, pp. 135-182 | Article | MR 3158627 | Zbl 1291.15088

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