English

On the Rank of Random Sparse Matrices

Probability 2007-11-20 v1 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.0711.2696,
  title  = {On the Rank of Random Sparse Matrices},
  author = {Kevin P. Costello and Van Vu},
  journal= {arXiv preprint arXiv:0711.2696},
  year   = {2007}
}

Comments

24 pages

R2 v1 2026-06-21T09:44:22.070Z