logo CRAS
Comptes Rendus. Mathématique
Probabilités
Singularity of random symmetric matrices – simple proof
Asaf Ferber 1
1. Department of Mathematics, University of California, Irvine, USA.
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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/crmath.215
Asaf Ferber 1

1. Department of Mathematics, University of California, Irvine, USA. 
@article{CRMATH_2021__359_6_743_0,
     author = {Asaf Ferber},
     title = {Singularity of random symmetric matrices {\textendash} simple proof},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {743--747},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {6},
     year = {2021},
     doi = {10.5802/crmath.215},
     zbl = {07390656},
     language = {en},
}
TY  - JOUR
AU  - Asaf Ferber
TI  - Singularity of random symmetric matrices – simple proof
JO  - Comptes Rendus. Mathématique
PY  - 2021
DA  - 2021///
SP  - 743
EP  - 747
VL  - 359
IS  - 6
PB  - Académie des sciences, Paris
UR  - https://zbmath.org/?q=an%3A07390656
UR  - https://doi.org/10.5802/crmath.215
DO  - 10.5802/crmath.215
LA  - en
ID  - CRMATH_2021__359_6_743_0
ER  - 
%0 Journal Article
%A Asaf Ferber
%T Singularity of random symmetric matrices – simple proof
%J Comptes Rendus. Mathématique
%D 2021
%P 743-747
%V 359
%N 6
%I Académie des sciences, Paris
%U https://doi.org/10.5802/crmath.215
%R 10.5802/crmath.215
%G en
%F CRMATH_2021__359_6_743_0
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

[2] Kevin P. Costello; Terence Tao; Van H. Vu Random symmetric matrices are almost surely nonsingular, Duke Math. J., Volume 135 (2006) no. 2, pp. 395-413 | MR 2267289 | Zbl 1110.15020

[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

Cité par Sources :