2007/11/16 by Kevin Costello, Van Vu, Costello, Kevin P. +1
Mathematics · #15A52 #60C05 #Advanced Algebra and Geometry #Combinatorics (math.CO) #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.0711.2696
openalex publication_date 2007/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This allows us to obtain an exact estimate for the co-rank.