Singularity of random symmetric matrices revisited
| Autor: | Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian Sahasrabudhe |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Proceedings of the American Mathematical Society. 150:3147-3159 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/15807 |
| Popis: | 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. 12 pages |
| Databáze: | OpenAIRE |
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