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Singularity of random symmetric matrices revisited.
- Source :
- Proceedings of the American Mathematical Society; Jul2022, Vol. 150 Issue 7, p3147-3159, 13p
- Publication Year :
- 2022
-
Abstract
- Let M_n be drawn uniformly from all \pm 1 symmetric n \times n matrices. We show that the probability that M_n is singular is at most \exp (-c(n\log n)^{1/2}), which represents a natural barrier in recent approaches to this problem. In addition to improving on the best-known previous bound of Campos, Mattos, Morris and Morrison of \exp (-c n^{1/2}) on the singularity probability, our method is different and considerably simpler: we prove a "rough" inverse Littlewood-Offord theorem by a simple combinatorial iteration. [ABSTRACT FROM AUTHOR]
- Subjects :
- RANDOM matrices
SYMMETRIC matrices
MATRICES (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 150
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 157053187
- Full Text :
- https://doi.org/10.1090/proc/15807