Hitting Time Theorems for Random Matrices

Source abstract

Starting from an n -by- n matrix of zeros, choose uniformly random zero entries and change them to ones, one at a time, until the matrix becomes invertible. We show that with probability tending to one as n → ∞, this occurs at the very moment the last zero row or zero column disappears. We prove a related result for random symmetric Bernoulli matrices, and give quantitative bounds for some related problems. These results extend earlier work by Costello and Vu [10].