Singularity of random Bernoulli matrices

• 成果类型: Article
• 署名作者: Tikhomirov, Konstantin
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.191.2.6
• 发表日期: 2020
• 页码: 593-634
• 关键词: invertibility; probability

摘要

For each n, let M-n, be an n x n random matrix with independent +/- 1 entries. We show that P{M-n is singular} = (1/2 + o(n)(1))(n), which settles an old problem. Some generalizations are considered.